Visual proof of sin(A+B) and cos(A+B) in one picture

[@sungymungy6930]

I have searched for an intuitive explanation of this concept, and I have to admit, this is very clear and insightful.

[@caitidowns6277]

I spent hours trying to find a more visual, intuitive explanation for the sum and difference identities and couldn't find anything beyond algebraic proofs (which helped a little to show where the identities derived from but did little to elaborate on their relationship to something tangible). Thank you for your video! I never comment on videos but this was such a big help to me and my understanding of this topic. So glad I found this before my exam tomorrow 🙌

[@bruhifysbackup]

Can you please share the algebraic ways you found?

[@tachles_math]

I couldn't agree more with u on the understanding part. Good video

[@zavianwilson6070]

I love this proof... its clear and clean.... its intuitive and insightful... let me state the obvious for anyone who is as blank as myself... each 90deg is composed of (alpha, beta and gamma)... once you identify any 'single term' in any of the triangle... the other angles are either a 90deg right angle... or a composition of the two missing terms... hope I helped someone.

[@davutselamiozkahraman8200]

Wonderful, easy and fluently proves. Especially I like it because you showed it with using unit circle.

[@adamsaher348]

Skp to 3:00 if you just want the proof without a lengthy into

[@randomindianguy3048]

I guess I am going to jail for a long time

[@Z00711287]

Thanks. One of best explanation

[@shivam-kharkhate]

Proof sin(a+b) in unit circle taking (a+b) greater than 90 degree

[@АйдарШакиров-х5у]

I am an abituriend from Russia and would like to glad you for this explanation

[@gaurav.raj.mishra]

Keep up the good work. Good luck for your KZbin career. We really need teachers with the kind of mindset you mentioned at the start of the video.

[@GSMusicMusic]

Very clear and very helpful, thank you.

[@DurgaraoRamakrishnaAdari]

Very nice. In single concept, two proofs are done.

[@tan1772]

this is a beautiful proof

[@the69paradise68]

..... طريقة ممتازة للبرهنة....... وتبدو سهلة لفهم كيف تستنج العلاقات المثلثية لمجموع زاويتين..... اعرف طريقة الجداء السلمي..... وتعلمنا طريقة اخرى...... لكن هذه جميلة جدا...... تعلمت طريقة المستطيل وحساب مساحات... داخل مستطيل.... الانترنات.... سهلت الكثير لمن يريد التعلم...... فكيف يكون الحال مع الذكاء الصناعي......!!!!؟؟؟؟

[@navindraarjunaabeyesekera7864]

Ingenious

[@JamesBlacklock]

Excellent!

[@Giga_Chad_2281]

its 1am and my brain is fried so quick question why is alpha in the green triangle?

[@joaofelipegueiros3743]

Awesome proof!!!

[@svojasmathsclassesbyvikass5564]

Beautiful explanation!

[@GyaneshwaranG]

loved your video! very interesting and elegant proof, and very clearly explained!

[@mathproofs4054]

Thanks a lot! Let me know what other theorems might be interesting for you, so that I can cover them in my later videos.

[@imeneeladel6471]

cos (a-b) please :'))

[@MedTronic73]

nice video good work .... please what is the name of the program you use

[@KevinLuke89]

I think it would help greatly if you could explain why you multiply inner sides to get the outside.

[@coldash7845]

6:37 why is it cosBcosA ?

[@coldash7845]

oh I got it. you explained in the beginning

[@siapaaja9360]

The radius multiple by cosB and got the adjacent B. Adjacent B = hypotenuse A, times by cosA and got adjacent A.

[@SunHail8]

great explanation.

[@trevorlim6148]

too good bro too good

[@simonwax7575]

Thanks very much for this. Very helpful.

[@sandrokavlashvili8617]

it is very good explanation

[@riteshkaran3841]

Nice explanation

[@TexasHoosier3118]

Excellent video. Thank you.

[@rnd_penguin]

Very sad to see you post no more,,,, what happened to you?

[@mrmaths126]

Which software is this????

[@ChechoColombia1]

Is this visual representation enough as a proof?

[@stephensewe4774]

Good and clear presentation. What app did you use here sir, I use geogebra but I can't use only symbols to represent the angles

[@pedrodelfino9493]

Keep the good work, great video!

[@168grhp]

Nice!

[@___llvm]

Very nice video.

[@BoZhaoengineering]

Very nice!

[@김충환-b8x]

훌륭한 가르침. 감사합니다.

[@888Antoine]

Beautiful work thanks :)

[@fellipeparreiras4435]

Mind = Blown

[@pbanerjee4008]

great job

[@ajmalrashid]

Nice Video Math Proofs. Very clear and vivid step by step explanation. Why don't you upload more? Which software (S) did you use by the way for writing/editing?

[@mathproofs4054]

Thanks a lot! Definitely will. What topics in mathematics interest you? I am planning to add the software used in the description, once I am clear with the legal issues.

[@devilking1366]

Excellent

[@rjsaha93]

THANK U VERY MUCH SIR! !

[@rubybhattacharyamathematic2896]

well explained

[@vishweshpalani1833]

Amazing

[@enterpriserx]

This is great but the real answer is when you look at a problem you see the square and reverse derive all counterrelations and sum or subtract when you need to get. Not for stupid people. Mnemnoics are just fine for

[@vaikunthchaudhari6041]

Thank you sir

[@xd-jy5ex]

thank you bro

[@frankhong6313]

Dude, that criminal/non-criminal comment is hilarious

[@science-y9209]

👏👏👏👏👏👏👏👏👏👏👏💛

[@AndriiBilous]

чітко! дякую

[@emilyyyyyym]

thank you

[@cyberjet5946]

Neat!

[@imeneeladel6471]

very good .great job but if u can do another video to proof cos (a-b) and sin(a-b)then u ll save my life

[@arunakumari3239]

cos(a-b)=cos(a+(-b)) sin(a-b)=sin(a+(-b)) Just use the same formulas but remember that sin(-x)=-sin x and cos(-x)=cos x

[@ganeshmishra4062]

Thx

[@manny4239]

This is because the teacher doesnt care to take the time to teach this to us

[@cloudunder1546]

oh i can see!!

[@alokgupta3006]

I am from India

[@vighnesh153]

you can work on your graphics more..

[@inxeoz]

Total ly green blur😭

[@Aman-br1ph]

Here i found mathematics

[@bruceedward3079]

The proof is hard to understand,

[@mithilaschoolofmathematics]

Just start on blank page by yourself ...by drawing a circle of any radius ...in anticlockwise dir take two Angels Alpha and bitha

[@eetswalads5528]

I only clicked on this video because I didn't have a unit circle handy ;)

[@mithilaschoolofmathematics]

This theorem cab proof by circle of any radius

[@christophersedlak1147]

thanks