Class - 11, Chapter 3, Introduction to Trigonometric Functions Maths || CBSE NCERT || Green Board

[@GreenBoard11and12]

Class 11th Question Banks-www.amazon.in/stores/page/53CA1F30-6D49-4CE6-A998-BA2BF30F3EEA?channel=Irs24-11qb-Green-yt Class 11th Sample Question Papers - www.amazon.in/stores/page/D3C6D06C-DD68-41A1-8C8E-A7570591DD01?channel=Irs24-11SP-Green-yt Intro to trigonometric functions - kzbin.info/www/bejne/sHipc6qVbah2m7s Ex - 3.1 - kzbin.info/www/bejne/pnzWZYCMbcynoJI Ex - 3.2 - kzbin.info/www/bejne/rZindYKhettrjZY Ex - 3.3 (Q1 to Q8) - kzbin.info/www/bejne/rZindYKhettrjZY Class 11 Ex - 3.3 (Q9 to Q16) - kzbin.info/www/bejne/bJPSmmeJbrh7bKM Class 11 Ex - 3.3 (Q17 to Q25) - kzbin.info/www/bejne/eKmzZXRsirtgZqc

[@Oppo-lv8ur]

Yes

[@mtraceryt6278]

Are 3.4 delete hai bhai

[@arihantjain8698]

Sir please upload exercise 3.4

[@deadlygaming3066]

60 degree =π/3

[@rohitkumarpandit5112]

Sir please next exercise jaldi se upload kar dejiye...bahut problem ho rahi hai...class me kuch samajh nahi aata...!!

[@marinecommando-xl3uh]

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant. Also, read trigonometric identities here. Table of Contents: Basic Trigonometric Functions Sine Cosine Tangent Cotangent, Secant, Cosecant Formulas Identities Table Graphs Examples There are a number of trigonometric formulas and identities that denotes the relation between the functions and help to find the angles of the triangle. All these trigonometric functions with their formula are explained here elaborately, to make them understand to the readers. Also, you will come across the table where the value of these ratios is mentioned for some particular degrees. And based on this table you will be able to solve many trigonometric examples and problems. Six Trigonometric Functions The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions. Consider the following diagram as a reference for an explanation of these three primary functions. This diagram can be referred to as the sin-cos-tan triangle. We usually define trigonometry with the help of the right-angled triangle. Trigonometric Functions Sine Function Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse. From the above diagram, the value of sin will be: Sin a =Opposite/Hypotenuse = CB/CA Cos Function Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. From the above diagram, the cos function will be derived as follows. Cos a = Adjacent/Hypotenuse = AB/CA Tan Function The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio. From the diagram taken above, the tan function will be the following. Tan a = Opposite/Adjacent = CB/BA Also, in terms of sine and cos, tan can be represented as: Tan a = sin a/cos a Secant, Cosecant and Cotangent Functions Secant, cosecant (csc) and cotangent are the three additional functions which are derived from the primary functions of sine, cos, and tan. The reciprocal of sine, cos, and tan are cosecant (csc), secant (sec), and cotangent (cot) respectively. The formula of each of these functions are given as: Sec a = 1/(cos a) = Hypotenuse/Adjacent = CA/AB Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB cot a = 1/(tan a) = Adjacent/Opposite = BA/CB Note: Inverse trigonometric functions are used to obtain an angle from any of the angle’s trigonometric ratios. Basically, inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions are represented as arcsine, arccosine, arctangent, arc cotangent, arc secant, and arc cosecant. Formulas Let us discuss the formulas given in the table below for functions of trigonometric ratios(sine, cosine, tangent, cotangent, secant and cosecant) for a right-angled triangle. Formulas for Angle θ Reciprocal Identities sin θ = Opposite Side/Hypotenuse sin θ = 1/cosec θ cos θ = Adjacent Side/Hypotenuse cos θ = 1/sec θ tan θ = Opposite Side/Adjacent tan θ = 1/cot θ cot θ = Adjacent Side/Opposite cot θ = 1/tan θ sec θ = Hypotenuse/Adjacent Side sec θ = 1/cos θ cosec θ = Hypotenuse/Opposite cosec θ = 1/sin θ Identities Below are the identities related to trig functions. Even and Odd functions The cos and sec functions are even functions; the rest other functions are odd functions. sin(-x) = -sin x cos(-x) = cos x tan(-x) = - tan x cot(-x) = -cot x csc(-x) = -csc x sec(-x) = sec x Periodic Functions The trig functions are the periodic functions. The smallest periodic cycle is 2π but for tangent and the cotangent it is π. sin(x+2nπ) = sin x cos(x+2nπ) = cos x tan(x+nπ) = tan x cot(x+nπ) = cot x csc(x+2nπ) = csc x sec(x+2nπ) = sec x Where n is any integer. Pythagorean Identities When the Pythagoras theorem is expressed in the form of trigonometry functions, it is said to be Pythagorean identity. There are majorly three identities: sin2 x + cos2 x = 1 [Very Important] 1+tan2 x = sec2 x cosec2 x = 1 + cot2 x These three identities are of great importance in Mathematics, as most of the trigonometry questions are prepared in exams based on them. Therefore, students should memorise these identities to solve such problems easily. Sum and Difference Identities sin(x+y) = sin(x).cos(y)+cos(x).sin(y) sin(x-y) = sin(x).cos(y)-cos(x).sin(y) cos(x+y) = cosx.cosy-sinx.siny cos(x-y) = cosx.cosy+sinx.siny tan(x+y) = [tan(x)+tan(y)]/[1-tan(x)tan(y)] tan(x-y) = [tan(x)-tan(y)]/[1+tan(x)tan(y)] Video Lessons Trigonometric Functions Session 1 1,087 Trigonometric Functions Session 2 701 Trigonometric Functions Session 3 15,687 Trigonometric Functions-Session 4 3,469 Trigonometric Functions-Session 5 3,094 Trigonometric Functions Session 6 2,426 Table The trigonometric ratio table for six functions like Sin, Cos, Tan, Cosec, Sec, Cot, are: Trigonometric Ratios/ angle= θ in degrees 0 ° 30 ° 45 ° 60 ° 90 ° Sin θ 0 1/2 1/√2 √3/2 1 Cos θ 1 √3/2 1/√2 1/2 0 Tan θ 0 1/√3 1 √3 ∞ Cosec θ ∞ 2 √2 2/√3 1 Sec θ 1 2/√3 √2 2 ∞ Cot θ ∞ √3 1 1/√3 0 Graphs By now we have known the formulas and values for different angles for all the trigonometric functions. Let us see here the graphs of all the six trigonometric functions to understand the alteration with respect to a time interval. Before we see the graph, let us see the domain and range of each function, which is to be graphed in XY plane. Function Definition Domain Range Sine Function y=sin x x ∈ R − 1 ≤ sin x ≤ 1 Cosine Function y = cos x x ∈ R − 1 ≤ cos x ≤ 1 Tangent Function y = tan x x ∈ R , x≠(2k+1)π/2, − ∞ < tan x < ∞ Cotangent Function y = cot x x ∈ R , x ≠ k π − ∞ < cot x < ∞ Secant Function y = sec x x ∈ R , x ≠ ( 2 k + 1 ) π / 2 sec x ∈ ( − ∞ , − 1 ] ∪ [ 1 , ∞ ) Cosecant Function y = csc x x ∈ R , x ≠ k π csc x ∈ ( − ∞ , − 1 ] ∪ [ 1 , ∞ ) Here is the graph for all the functions based on their respective domain and range. Trigonometric functions How to Solve Trigonometric Functions? Solving Trigonometric Functions 6,099 Solved Examples on Trigonometric Functions Example 1: Find the values of Sin 45°, Cos 60° and Tan 60°. Solution: Using the trigonometric table, we have Sin 45° = 1/√2 Cos 60° = 1/2 Tan 60° = √3 Example 2: Evaluate Sin 105° degrees. Solution: Sin 105° can be written as sin (60° + 45°) which is similar to sin (A + B). We know that, the formula for sin (A + B) = sin A × cos B + cos A × sin B Therefore, sin 105° = sin (60° + 45°) = sin 60° × cos 45° + cos 60° × sin 45° = √3/2 × 1/√2 + 1/2 × 1/√2 = √3/2√2 + 1/2√2 = (√3+1)/2√2 Example 3: A boy sees a bird sitting on a tree at an angle of elevation of 20°. If a boy is standing 10 miles away from the tree, at what height bird is sitting? Solution: Consider ABC a right triangle, A is a bird’s location, B = tree is touching the ground and C = boy’s location. So BC 10 miles, angle C = 20° and let AB = x miles We know, tan C = opposite side/adjacent side tan(20°) = x/10 or x = 10 × tan(20°) or x = 10 × 0.36 = 3.6 Bird is sitting at the height of 3.6 miles from the ground. Trigonometry Related Articles for Class 11 and 12 Trigonometry Formulas For Class 11 Trigonometry For Class 11 Trigonometry Formulas For Class 12 Trigonometry Table Register with BYJU’S to get more such maths-related articles in a simple and detailed way. Also, register at BYJU’S to get access to 1000+ hours of engaging video lessons for different subjects and classes. Frequently Asked Questions on Trigonometric Functions Q1 What are the six trigonometric functions? The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant and Cotangent. Q2 What is the use of trigonometric functions? In geometry, trigonometric functions are used to find the unknown angle or side of a right-angled triangle. Q3 What are the three basic trigonometric functions? The three basic trigonometry functions are Sine, Cosine and Tangent. Q4 What is the formula for trigonometry functions? If θ is an angle of a right-angled triangle, then the trigonometry functions are given by: sin θ = Opposite Side of angle θ/Hypotenuse cos θ = Adjacent Side of angle θ/Hypotenuse tan θ = Opposite Side of angle θ/Adjacent cot θ = Adjacent Side of angle θ/Opposite sec θ = Hypotenuse/Adjacent Side of angle θ cosec θ = Hypotenuse/Opposite Side of angle θ Q5 What is the value of sin θ, cos θ and tan θ, if θ=30 degrees? If θ = 30 degrees, then, Sin θ = sin 30 = ½ Cos θ = cos 30 = √3/2 Tan θ = tan 30 = 1/√3 Q6 What is the range of sin, cos and tan function in a periodic graph? Sine Function: y = sinx; Domain: x ∈ R & Range: − 1 ≤ sin x ≤ 1 Cos Function: y = cos x; Domain: x ∈ R & Range: − 1 ≤ cos x ≤ 1 Tan Function: y=tan x; Domain: x ∈ R , x≠(2k+1)π/2 & Range: − ∞ < tan x < ∞ thank you i can explaint it well without explainting

[@ProAshplayz]

you copy-pasted this didnt you

[@xysskills638]

Bro u fking copy pasted it the English in paragraph and in the last line are very different 🫵🏻🤣

[@ayushsharma7216]

Well done

[@sugandhakumari-m7r]

i better die before writing this much🤣🤣🤣🤣🤣🤣

[@marinecommando-xl3uh]

@@sugandhakumari-m7r not written 'pasted' i was irritated by his explaination so i dropped it down here

[@lakshaysaini8965]

Sir you teach better than my school teacher😂😊❤

[@age.ofgamer]

You are right bro😂😂😆

[@sarthakpal8727]

11th me school teacher bhi student ban jata 🙂

[@studywithraghav9563]

​@@sarthakpal8727😂

[@sarthakpal8727]

@@studywithraghav9563 raghav bhai ye real body hai tumhari

[@Akash___Gamerz]

​@@age.ofgamer😂

[@bhavishya6452]

60° in radian = 360°=2pie Divided by 6 both side 360°/6=2pie/6 60°=pie/3

[@itz_yeastic]

or you can do it in this way too pi = 180 degree 180/3 = 60 degree (divide on both sides) therefore pi/3 = 60 degree

[@goldydubey3856]

Galat ha 😂😂

[@saranyaaa1305]

@@goldydubey3856 yes

[@Jaishreeram35785]

Right answer bro

[@NeonNickYt]

​@@goldydubey3856sahi toh hai mdc

[@MeghaSK-tx2tu]

Thank you so so much sir..u covered all the topics within 40 min .. thanks a lot

[@BBunny0122]

Thank you sir .... Your explanation is so well ... Helped a lot ❤

[@__umeshh.07]

I have a good result for class 10th for KZbin green Board thankyou Mandeep sir

[@ManikSharma-cw2qi]

Es chapter ke formule itne zayda h chakkar aa gya😳

[@Pure_Gamers]

21 hai total

[@Priya-gn1xr]

😢😢😢​@@Pure_Gamers

[@KhemThapa-bg7jg]

Hm

[@ashutoshsingh3777]

34 hai total

[@surendersheoran6786]

Ye kuch nahi tere to is sa bhi zayda baap ha

[@selection_2027]

To convert degrees to radians, you can use the formula: \[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \] For a 60-degree angle: \[ 60 \times \frac{\pi}{180} = \frac{\pi}{3} \] So, 60 degrees is \(\frac{\pi}{3}\) radians. Like the comment please 🖐🖐❤❤

[@lakshyapratap2522]

CLASS 12 MAIN HE WO BI BOARD SIR TO USKE LIYE VIDEO LAOGE TO APKA CHANNEL OR GROW HOGA

[@age.ofgamer]

Sir kya hi padhate ho wahh apka jawab nhi sir jiiie😆😆

[@anishmahajan420]

Jaii shree rammmm🚩❤👀❤️‍🔥💥

[@sumankumari4584]

Pdhle gadhe spam krne ki vajaya

[@roasterfan]

🫡

[@animanattadas7133]

Jai shree ram ❤

[@amanpreetsingh4644]

Sir, your videos are really great and useful, but sir class 11 has a huge syllabus. Please try to cover syllabus fast, everyone in 11th must cover whole syllabus before september at least for IIT aspirants. Thereby I request you to cover maths fast, plsssss

[@Mandeepkr]

I will try👍

[@BhuvanaHiremath-bk3ud]

​@@Mandeepkr sir pls make video of therom related to this chapter pls sir

[@MeghaSK-tx2tu]

Sir can you please tell me why at 31:35 sin(π/2+x)= cos x? Shouldn't it be -cos x as it is in the second quadrant

[@khushijain8449]

Same doubt

[@gulshan7990]

​@@khushijain8449 Same doubt

[@SaM-xt1eg]

Same bruh

[@animekoibito565]

Bro because cos is negative in 2nd quadrante

[@zubu_editz]

Batao yaar

[@Rohitvermaff]

0:32 Angles. 1:01 positive angle. and negative angle. 3:20 Degree measure 5:40 Radian measure. 7:26 national convention 12:56 Trigonometry functions 33:33 Range of trigonometry function 34:58 trigonometric formulas. 37:48 The end

[@ShreyaYadav-d18]

Thanku brother ❤️

[@rohitkumarrohitkumar5457]

Sir you are very genuineness sir 😊i don't understand lesson 3 any teacher but I 💯 percent understand watching after your video ❤

[@HAWK2007]

Appreciate your English

[@Raghuraii]

lol bro is pro @@HAWK2007

[@HAWK2007]

@@Raghuraii fr

[@Abcricinfo00007]

Batch 2024 attendence here👇

[@MadhumithraSenthil74]

why started 3rd chp directly?

[@ashtragaming5986]

At 16:47 if you think its hard to remember after school to college . then you can remember it by (add sugar to coffee ) I used this its easy to remember

[@fftrikergamers7255]

😑😑😑😑😑

[@iVin_6969]

​@@fftrikergamers7255bhai chut nhi mil rhi mujhe

[@bearop8937]

Abeee toh "after school to college" Me konsa JEE ka concept lg rha h ye bhi easy h isme yaad kya rkhna?

[@Scrollwithme_2k24.]

Ye toh alakh sir ne bataya tha😅

[@RihanMudigere]

All student take cigarettes

[@anjalimalviya455]

Sir you are best explanation for math subject

[@VANSHSINGHRAJPUT-hu2ix]

All legends watching this 1hr before of exam😂😂

[@Jai_hind.-]

THANK YOU VERY MUCH SIR FOR THIS WONDERFULL VIDEO🙏🙏🙏☺

[@arhgamingworld_99]

Legend watch in October 😅

[@shivanRawat-zq7vh]

Yes bro 😂

[@TrishaTanyadass]

No Legend watch in November 😂

[@AizaShethi-y1f]

​@@TrishaTanyadass true af

[@NittanSingh-Z]

9 November

[@mokshsharma2845]

November

[@Gannusharma-z3e]

Thankyou sir for giving us this knowledge sir y you are a brilliant teacher sir aapke vajeh se mere 99 marks hai maths me

[@satendergahlyan]

Sir aap pdha too acha rhe ho per muje nind aane lgi zese sir pdhate h. 😅🤭🤤😴🤤

[@Abc_438]

True

[@CodeCurrent-2708]

MUGHE TO NAHI AATI COOFEE PIYA KARO

[@tsdkr1566]

Instead of using the trick ' after school to college ' i prefer to use 'Add Sugar To Coffee' it can be more easier to remind....

[@i_identify_as_an_egg]

I prefer "All Silver Tea Cups" Our teacher taught this to us

[@rahatrehman]

Love your teaching ❤

[@SumanKumar-de1wu]

Thanku so much sir for nice explanation 🙏🏻🙂

[@ronakmeena2457]

Tq so much sir aap bhut accha padte ho 😊

[@NehaVashisht-t4t]

The way when he said, "2 darjan se jyada formulae" 😂❤

[@Ytdarkworld]

😂😂

[@Vibhavsinghrawat]

The way your parents gave birth to a disappointment like you ❤😂

[@arnktech_01]

Maine suna tha ki jyadatar ladkiya math nahi leti?

[@Sana-ni6qp]

​@@arnktech_01bhai sahi suna hai apne par kuch leleti hai meri tarah

[@arnktech_01]

@@Sana-ni6qp tumhari choice mai isme kuch nahi kah sakta

[@Ayush-088.5]

So beautiful lecture❤❤

[@premraaz6053]

You're a masterpiece

[@RameshJangra-v9h]

Sir 5 ka chapter please 😢

[@Ignitethoughts07]

180°÷3 = Pie which is 180 also divided by 2 then we get 60°=180/3

[@Priya-gn1xr]

Good❤❤

[@divyakitchens5875]

Sir ek chiz kehni hai Aho bhagya hamare jo aapne yeh introduction video bana hi di aakhir bus sir ab aap hame jaldi jaldi or bhi line by line sare chapter ki video bana dijiye and thanks for this 😊

[@siyavishwakarma297]

11th wale atendance here😊😊😊

[@PoonamSharma-eo6dn]

34:55 Gangsta Arrived 🗿🗿 Plot twist😅😂😂

[@poojapal4839]

Sir your teaching style amazing

[@deathbed_16]

Yupp, Same

[@samruddhijadhav827]

Thank you sir JAI HIND

[@amandeeprai6200]

Thanks sir and teachers day🎉🎉

[@vijaydutta8799]

Best sir for teaching love you❤❤❤😊

[@maurya252]

2024-25 wale attendance lgao 😂😂

[@Userdg4775]

Bhai fatti padi hai yaha 24-25 me 😢

[@maurya252]

@@Userdg4775 us bro us 🫂

[@dilshaddilshad6558]

Sir, I'm doing well in maths just because of your amazing teaching skills! Thank you!!!

[@AnshTiwari91]

Kis kis ka kal UT HAI 😢

[@M.RITWAL-in9ho]

Sir please upload all chapter vedio 11th and 12th class because sir many family haveing face a financial problem and not able to pay a tustion fees but with the help of your vedio student solve the math very easily and free of cost so i humbly requsted to you sir upload the all vedio as soon as possible 🙏 So sir please make fast and upload the all vedio fastly before the march exam🙏🙏

[@Ratanbro108]

Who all came here after class 10 board exam and wana start new session 2023 form this channel 🥰🥰

[@its_queen849]

Me

[@abhithakur3733]

Me

[@its_queen849]

@@abhithakur3733 10th me kitni result ayi

[@Mr.GamerX13]

88.5%

[@killersquad4413]

Mere 72 %ayye😅

[@anilkadian1317]

Green board class is very important 😁☺️ for cls 11th 🎉🎉😊

[@anilkadian1317]

Hii

[@anilkadian1317]

You must she

[@anilkadian1317]

🙂

[@anilkadian1317]

Your name

[@anilkadian1317]

Kon 😮😮

[@___thakur_ansh]

Jinko lagata hai sir accha padate hai like kare

[@ruchithaacharya3912]

Sir ur the best ❤🎉

[@itz_sonu_edits1857]

10:38 ans ) 60 degree convert into redian=, π/180 × 60 = π/3 -----

[@khanayan786-c1n]

PCM Wale Attendence Here 😅😅

[@rameshsen5697]

Ayan Khan

[@GhazalSetia]

Present 😂🤌🏻

[@khanayan786-c1n]

@@GhazalSetia 👋👍🤗

[@GhazalSetia]

@@khanayan786-c1n yupp

[@butsathya7324]

Absent

[@JKGurus]

Sir u r the best teacher ❤❤

[@ArijeetAich-iv5wp]

Sir miscellaneous bhi karba do na 0:01

[@NiteshSharma-m7x]

Kon kon kheta Hai ki Mandeep sir is best maths teacher other chanel maths teacher ❤❤😊😊😊

[@pinkysorout8805]

Thanks Sir I got 100 marks in math in 10th class

[@fftrikergamers7255]

Schme 😊😊😊

[@technicaltukkugaming7600]

Sali lier

[@Hitlur.my.buttler]

Really?

[@RakehsKymar]

Me 99

[@shinthedwag00]

I won't lie I got 40% in maths (obviously with intervals)

[@Aditya_Gamerz_technow]

Keep making this video sir 10th bhi appse padi he abb 11th aur 12th bhi bass app video banate raho

[@PoonamDevi-u9r7p]

Sir kb se aapka channel dund rhi thi finally ab mil gya h 😃😅

[@shubhamsaini6629]

90° multyply by 2/3and nest side Π/2multply by 2/3 so 60°=Π/3

[@JayoshiChakraborty]

Thank you sir, apka videos mujhe 10th mein bhi help kya or abhi bhi bohot help kr raha hain.... your are legend sir🙏🙏🙏

[@pradhankhants927]

Bahut maja aya thank you so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so 😅😅 much 😊

[@amitrajput_ff]

Today kids says who is legend ❤ I say Mandeep sir ka naam suna hai😂

[@Kapil-x5n]

Thankyou sir for best explain

[@doctor119kAS]

Thanks so so much sir u are back plzzzzzzzz sir complete class 11th all chapters plz sir when I see u are live I was so happy I swear

[@divyakitchens5875]

I am also very very happy 🥰

[@Chetan77712]

Right

[@JoyPaul-zo9nw]

Thank you sir ❤🎉

[@gwbrother1]

10:45 PIE/3

[@anilkadian1317]

Thank you so much sir for nice explanation 🙂👍☺️😁😊😌

[@HobbieHouse]

THANKYOU SIR 😇😇😇😇😇

[@mr.aryanyt1548]

So cute.......... U are ❤❤

[@singhankit71]

Wow super sir🎉🎉❤

[@dakshachuchanRorMaratha62]

Thank you so much sir , bahot zarurat thi iss video ki❤

[@Pain..09]

Add Sugar To Coffee 17:15

[@NehaVashisht-t4t]

When I understood trigonometry in 10th, I took Arts with Math in 11th, but it has a different system 😂 who agrees ❤️

[@meerakumari4410]

Same😂

[@mankamnavishwakarma2418]

Sir I got 80 persent and I had studied form you thak you sir❤😊

[@Mr.Paheli.131]

Sir please complete whole syllabus fast

[@_NAMAN_]

Phli bar itna khush hua me😊

[@avishnaik817]

Actually sir it's notational convention, not national convention! , anyways you teach good 🎉😂

[@aditeevenikar]

sir please make videos on other chapters also especially on limits and derivatives and straight lines🙏🙏

[@sanjaydutta4382]

Bhut aache pada te hai sir

[@vanshpunia6437]

Sir aap class 11th k Sare chapters jldi se jldi laiyee Or koshish kree ki agla chapter complex number hoo

[@_Short_with_me_]

Ultra Pro max legends are watching in November 😂

[@VANSHRATH1]

Bro, I am watching in December 😂😂😂

[@anilkadian1317]

👍 Aall 👍 of 👍 these 👍 students 👍good 🤞 🤞💯☺️😊😌luck for clas 11th nice

[@GurpreetSingh-pq1cf]

Very very amazing vdo sir This vdo is very helpful for us Thank u so much to make this vdo ❤❤❤❤ Thank you so much sir You are the best teacher

[@Lovelygirl972]

180/3=π/3 60=π/3

[@studyinggg2471]

Mathematics Chand dekhna h / pie dekhna h / perimeter area circumstance dekhna h / 9.18 180 90 360 kaisa 2,3,4 se dono side divide krne p aara h wo likhna h copy m / trigonometric table.

[@HallanfamilyHallan]

Anyone from PCB to for better understandings 😊

[@MagicWorldCreation99]

Sir you are god teacher

[@amanchhikara001]

16:12 16:14 16:14 16:15

[@LuckyBisht-u3s]

Legend watch in today paper

[@AnjaliPunekar-ge4cu]

Its just amazing 🎉❤️‍🔥

[@rkrm2007]

Very very thank's sir .only after listening the introductions of chapters that you have provided I have completed my all the exercises. But since last time you haven't provided the introduction of chapter 3. Now I am completely relaxed and very much happy when I see the notification in my mobile of your this video..

[@RUDRAKAH]

Bhai sat sat naman usko bolta h jo mar gaya ho apna sir to inmortal h bhai

[@CRICKETLOVER1700-id2mm]

(60° in Radian) ??? =180° = π radian = 1° = π/180 radian = 60° = π/180 radian = Dividing = 60°/180° (Now)= 60°= π/3 radian Ans.

[@bluebag7179]

Bhai mai 11 mei fail hoke bhi re exam deke pass hogya aur ye bhai ki video aab drop ho rahi hai😍🤌🏼

[@SitaDevi-lf9wp]

Thankuu so much sir ji bahut din is ki jarurat thi

[@FREEFIRE-qp3el]

Sir .... u're such an amazing teacher ........ U're using very simple methods nd .....that is a great speciality in ur teaching ........thnku so much 🩷🩷

[@DiyaBharadwaj-cl9pw]

Sir please regularly upload kijiye saare chapters. Me aapke hi bharose hu sir🙏😭

[@art_by_gayatri1266]

Sir chapter 4 ki videos bhi upload kijiye please 💝.... You are the best teacher 💞

[@abhishekkaprawan]

Thank you so much sir🙏❤️

[@marveleditverse.]

I've got 92 in maths in board by studying whole 10th by Green Board

[@youtubereels2284]

CBSE Or state???

[@marveleditverse.]

@youtubereels2284 CBSE ofcourse

[@SidT-di4fr]

okay, who asked though?

[@TUSHARYADAV-vr3en]

Sir you are great

[@Jimis__live]

No one can explain like him literally 😊

[@Nargis-tz2qf]

😊😊😊 very nice

[@IshaBharti-vz5xl]

Sir please class 11 probability pe lecture banado sir please🙏🙏

[@Gaming_skills01]

Yesss

[@Gaming_skills01]

Ab sir nhi dekhenge ye 1year old video h😂😂😂

[@ShinChanTube]

Love you bhaiya❤❤❤❤🎉🎉🎉🎉😅😊

[@muizzhannantravelvlogging8631]

Hi 2024 attendance ❤❤❤❤❤❤❤❤