Verifying Trigonometric Identities Easily - Strategy Explained (14 Examples)

Learn how to verify trigonometric identities easily in this video math tutorial by Mario's Math Tutoring. We go through 14 example problems involving reciprocal identities, quotient identities, even and odd identities, pythagorean trig identities, and cofunction identities. I also share tips for how to approach verifying these trig identities.
Related Videos to Help You Succeed!:
Verifying More Trig Identities
• Verify Trig Identities...
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[@kristina-we7mm]

Just wanted to say thank you for that kind message at the 9 minute mark, I'm in pre-calculus and although I try my best in math- i always need to put the extra work in to be able to score well in the class so I spend extra time watching videos like this to practice & understand better. This was definitely helpful and very clear to understand thank you!

[@MariosMathTutoring]

You’re welcome Kristina! Keep up the good work!

[@lazyonigiri5665]

@@MariosMathTutoring that massage changed my mood and it definitely helped, tysm

[@MariosMathTutoring]

You’re welcome!

[@aperson6966]

@@lazyonigiri5665 *message

[@kanemurfin8159]

You're not alone, I am in the same boat and I really appreciated both of your remarks.

[@jacobsteel130]

What i really appreciate is the fact that you say each step even if it’s kinda repetitive. I have problems with my teacher assuming I know things and skipping steps, making it impossible to learn how to complete these problems. Great video!

[@jinnycho9270]

Love it when teachers do ACTUAL examples Thank you!!

[@nikoflow_fm9541]

Right… when my teacher gave us practice problems, they were WAY easier than the ones on the test. So it took me by surprise and I did poorly. I hate when teachers do that :/

[@MA-zo3cm]

On my first attempt I couldn't even get one. Then I watched other videos and studied more. On the third or 4th day of trying I attempted it and got 9/14. Today I tried it again and can do all 14. This really is about experience. There's only so many kinds of problems they can show you, eventually they'll be forced to repeat the same kinds of problems. Now when I see a problem I know what to do because I've seen all the tricks. Keep doing this, build experience, and keep an eye out for patterns. I must have sunk over 20 hours into getting this concept as someone with a normal intelligence over about 5 days, so keep that in mind as you struggle! This is hard, it's supposed to take a long time.

[@zohaibhassan815]

this makes me feel so much better because this concept is so time-consuming and I don't even understand anything right now.

[@yahboi_mo]

I’m not even learning this yet but at least I know where to look if I need it. Thanks man

[@MariosMathTutoring]

You’re welcome! Glad you like my channel!

[@maxamedyuusuf6593]

@@MariosMathTutoring please teacher send me your what's upp Number

[@Mariam.4445]

I've struggled with this topic for months, and now before my exams starts, I can proudly say that I was able to solve all of them correctly!!!, I used to just stop in the middle, not knowing what the next step is, but now i don't just solve, I have different ways than the video that had given the same answer!, thank you, ALOT.

[@ishke2994]

How do u do it? Whats the other ways

[@Mariam.4445]

@@ishke2994 well it’s been 9 months since I commented, but I guess it’s fine, The way to solve these equation is to simplify it, thought there are a lot of identities as written as written on the right of the board, I think what I meant here was that I used a different one of those, but ended up with the same solution.

[@nathanielabel9874]

why cant my teacher explain concepts well like you. THANK YOU

[@sab.a3557]

I'm doing this in A level maths in UK. Hardest topic I've come across so far.

[@bro...5849]

What’s A level mean? Is that like honor’s or something? Not in UK so idk lol

[@sab.a3557]

@@bro...5849 A-level is what UK students study in college for 2 years (HIGH SCHOOL IN USA) You pick 3 subjects, i.e. Maths, busienss and Law then move onto university 2 years later

[@naushadharji8930]

Trigonometric identities are the EASIEST of the topics in mathematics !!!

[@sab.a3557]

@@naushadharji8930 maybe for you. Remember we all have strengths and weaknesses in different topics. You may find a topic hard that I find relatively easy. 👍

[@beningram-eiser6121]

@@naushadharji8930 bro fuck you this shits hard

[@shrekswife3755]

i have a test on proofs in two days and i can’t do them i’m gonna cry 😃 edit: so uh update....i got an F on it 😎

[@script_kiddie_1394]

u cute lil bitch

[@jaredr9469]

hahah mine is tomorrow. I think i will fail too :D

[@noisyguest5249]

@@jaredr9469 bruh same

[@bishlasagnaga5626]

We all fail together :')

[@swisherodocus314]

I passed so idk why im even here lol

[@andrewhart9913]

It’s always nice when you get trig identities that can be proven by expanding and factoring, or making due with what’s already written, but it gets trickier when you get ones that you have to multiply by external terms through multiplying by 1, such as multiplying one by (1-sinx)/(1-sinx).

[@elsalailanisadang6155]

I'm so thankful that you posted a vid about this topic. I was crying lately since I really don't understand, yet I smiled when I suddenly learned this topic all thanks to you. Thank you so much! God bless you sir.

[@letsplaysomegames985]

You are a life saver, this unit is just thinking out side the box and explained it perfectly.

[@Full60]

There are a few good channels out there that teach this topic, but yours was the easiest for me to follow, and the most helpful. Thank you.

[@チーズ-l2m]

This is some gold man, i really like that youve listed down the identities on the side too

[@BoZhaoengineering]

Probably the best precalculus on KZbin! Thank you for these examples !

[@dreivonfunf9489]

First time through this video, I got 2 on my own. Second time through I was able to get 11 out of 14 on my own. (It really helps if you pause the video before he explains it and try it yourself. And watch this video more than once. ) Thank you sir for making this videos!

[@cocoa_cake]

i looked through so many videos on this topic but you're the first to have actually helped me with this!! thank you so much

[@alexisflory6496]

Number 7 is on my actual homework and now I actually know how to do it... Probably going to just save this video and hoard it with all the other videos I have for precalc

[@tuckerschutte8165]

Very thorough and helpful video!

[@MariosMathTutoring]

Glad it was helpful!

[@JustinGarfield1]

I really enjoy this although I'm new to this and I have been doing a self study of mathematics for only 2 years. It appears once you memorize the formulas you can understand it easily and internalize it and truly understand it. And it's very true what you have said in the video: We need to look at the answer while we position our calculations on the other side of the equal sign. I had to learn the hard way after a few tries. This sort of reminds me of a Rubik's Cube. Your teaching skills are more clear and organized than most instructors I've listened to. thank you

[@marieyamabukhalil6631]

I did my whole assignment right because of this video thanks alot ❤ sending love from Egypt.

[@isabellapearlstein9896]

Thank you for this explanation. My teacher does not explain things well, he just gets annoyed with us and keeps repeating the same thing that is not helpful. He refuses to explain things any other way so it is nice to be able to watch your videos and have the material actually explained. I have a final tomorrow and we haven't learned everything that is on the packet so thank you for explaining the trig topics that we didn't really learn.

[@gloryhniang6125]

This youtube channel is so helpful. This makes doing math during Covid time much easier. 8:16 God bless you, Mario

[@elirhoades103]

Thank you for the encouragement message for number four. I was just about to quit but you helped me. Thank you. We need more people like you.

[@kevinburns8473]

Thank you tremendously, with the onset of Covid-19, I feel a lot of professors have gotten lazy. I am only allowed into my math class once a week, on a Monday and ALL of my course work, including the tests, are due online through a third-party program that costs extra money... I appreciate you picking up the slack that my professor has created.

[@redcurated4302]

Super helpful! Right on the spot of how difficult my HW is, he explains all the "secret sauce" moves my teacher uses.

[@jaineilsart1528]

At first this was hard, so I stopped doing this for a looong time. But your perspective changed my mindset mathematically, so mathematically by now, I should be able to do most of these by myself all thanks to u

[@scottpalmer829]

You have some of the best videos of any YT math teacher. I have profited from your videos in several math subjects.

[@MariosMathTutoring]

Great to hear!

[@scottpalmer829]

I'll try not to comment too much, but your point about experience is crucial. After practicing a great deal, you get a kind of intuition while looking at an identity. For instance, on your fourth example, I saw the 1 - cos and immediately thought "conjugate". I went that way, ran into a road block and then tried a different route and ran into a road block. I then went back to the conjugate and got it. Your comments about verifying identities are spot on.

[@jessemiller1135]

Thank you so much, Mario!! This video was a lifesaver right before my finals.

[@ryvan3870]

Thank you, your explanation helped me. These are actually pretty fun now that I know what to look for.

[@MariosMathTutoring]

Glad to hear!

[@laylaa259]

I just wanna say THANK YOUUUU, I'm going to an exam in 10 minutes and a classmate sended me this video. Thanks to this video I at least will get an acceptable note, because I didn't understand anything, and now yes. SO THAAAAAAAAAAAAAAAAAAAAANK YOUUUUUUUUUUU, you have my suscribe

[@crake9510]

thank you so much MARIO. you are the BEST teacher ever

[@Dylan-ur1oc]

got my pre calc quiz tomorrow, I appreciate the review

[@jameslawrencedelacruz543]

Thank you very much sir! You are helping struggled students like me!

[@Theright_court]

Dude Mario you're the goat, I owe all of my knowledge to your excellent teaching.

[@MariosMathTutoring]

Glad to help

[@Elitea20]

I got 0/14 correct, but I learnt how to do them after you did it thanks a lot

[@arundhatic.2792]

So helpful; got an A on test thanks to your videos!

[@Nellympacheco_]

Thank you soo much! I understood a lot more quicker and better watching this video

[@vadersz]

I have a test today and so far I have aced every test since algebra with your vids thanks

[@magl1609]

This man is a national treasure.

[@Gjaiiajna]

*i am 10 standard 👩🏻student in india* 🇮🇳 *i literally like to study maths subject from your channel* Thank you so much sir 🙂🙂🙂

[@Curiousbatling]

Thank you so much for your videos. This has been really helpful for me as I try to get through this trigonometry class at my college.

[@MariosMathTutoring]

You're very welcome!

[@themadirish8202]

This was really helpful, thanks for the 14 examples as well.

[@daphneb6905]

i’ve been struggling so much with these! This video helped a lot thank you!

[@josiahgoshert5023]

Thanks so much for the examples! Extremely helpful!!! Worth it to subscribe!

[@MariosMathTutoring]

Glad it was helpful!

[@alexnajera1821]

Thank you so much for this Mr. Mario. I had a test today and I think I aced it because this video really helped me understand the different strategies to solve each problem. My teacher wasn't nearly as good explaining as you. I'm sure to use more of your videos to help me do good in the class. You're a legend! 😁

[@alphax395]

Thanks Sir! Please try to make more verifying videos and complicated as well!

[@phlegmsmoothie]

I am a 10th student in India, this really helped me and all those problems were directly suited for ICSE.

[@effiegiannoudakos3286]

hi sir, you may have just saved my whole algebra 2 grade, thanks so much

[@stodgierpage7949]

My algebra II class is killing me with these verification! Thx so much for this vid!

[@patiencekamwo5394]

Thanks, your vedio remouved from my mind the fact that trigonomatry is difficult!

[@gyzzaortizperalta3962]

I genuinely love this guy

[@emma-sk3zy]

thank you so much for this video, it helped me a lot and you have taught me more in 30 minutes than in a month in school:)

[@joeldoxtator9804]

The most useful part here for me was the tip to not factor conjugates for the numerator. That was the whole issue I was having in seeing eliminations that could be made.

[@kanakabidarkar4333]

Even tho i am not an expert... just a tip... Try noting down al the techniques he is using ... it was super useful for me Thanks !

[@Panzer-jx2nv]

Thank you so much, I was working along with these examples. These can be so dang mind numbing but this video certainly helped me push forward.

[@troy2192]

Thank you so much. Saved my sanity with the great teaching! Have an awesome day.

[@Dallinjeshua2009Dallin]

Dallin here .. watching this from india ..Very useful one thank you

[@MariosMathTutoring]

You’re welcome!

[@brainstew21]

Underrated video

[@chérie-ta]

thank you so much for this thankfully i'm not struggling as much as before in this topic. i even got excited when i answered one question correctly. Thanks to you!!!

[@ProfIqbalHussain]

Very useful lecture and explained very well. I shared it with my BS Chemistry students.

[@yourfriendlyneighborhood8663]

That's a lot of examples. Thank so much sir.

[@ymcmb_sushi]

Thank You for teaching me this.

[@farishani4626]

Sir you look like Charles Xavier... Thank you sir for your teaching

[@glofevillemay4844]

Today's my final examination for trigonometry and I hope I'll apply on the exam what I learned in this video. Thank you

[@curetonbenares9236]

how did it go

[@shannonmarlyse4642]

YOU are my FREAKING HERO!!! Thank you, Thank you... 🤩

[@victorpaz5585]

Mario saving my day once again. Thanks so much for the awesome video

[@ssjsssssssssssssssssssssss6183]

this actual so much helpful wish my teacher can explain more specify

[@esmeralda9712]

You are saving my life right now😭

[@randomtori1878]

Great for review! Thank you!

[@kennadycotton9340]

You are the absolute best!!! Saved my life! Or at least my grade🤣

[@galineldho2063]

This was a great video that has helped me lots! Practice was great.

[@sanuratennakoon7979]

Thank you for posting this great video

[@entropy3705]

You're an absolute life-saver!!!

[@evangelistajohnfrancis5704]

You are a great teacher Sir. Mario

[@Foghcrn]

Watching this 4 hours before my exam in the middle of the night. Thanks

[@abdulrahmanalabbasi6559]

Thanks man a lot, you don't know what have you done!

[@MariosMathTutoring]

Glad I could help!

[@honey_boi69]

4 years later and this man is helping me cram so I pass my high school pre cal exam. He deserves an award for being so helpful

[@MariosMathTutoring]

Thanks!

[@crunchyteardrops4663]

I went into this confused and frustrated as to why I kept getting my answers wrong. (even though I felt I was doing everything I could) This video helped me realize that I was disregarding 2 of the Pythagorean identities 😂😂😂😂 No wonder it was so hard. Thank you so much for the help and positivity. We need more teachers like you.

[@kennethkare4054]

Thank you! this video has been very helpful..👍

[@hoffin5729]

Thank you man this has been very helpful.

[@teddadolphson4237]

I believe people have an identity that is deeper than sexuality. Some are warriors, creators, and healers but without teachers, no one would make it that far. Teachers are the most valuable resource in our world.

[@user-ig4cb5bl1d]

Wow. This is awesome! I wish all math videos were created like this where his words are actually on point. Worked 4 problems so far and my answers where right and working logical it's just that I found alternate workings for 1, 3 & 4. Could I still be correct?

[@user-ig4cb5bl1d]

@Paris Prasad sure about that? There have been instances where at the end I proved the identity yet my workings were wrong. I did consult a teacher to confirm my answers and they were right.

[@いくら-k4h]

thank you so so so much! this helped me a lot for my assignments

[@sydneywilliams1536]

working with you is so fun

[@cre8tivesriram342]

You are the best maths teacher I have ever had. Previously I got Fail Marks on Mathematics 14 out of 50. But now I can feel the adrenaline pumping to aim for the bull's eye. Love from India 🇮🇳

[@bobmilton907]

क्या तुम पास हो गए?

[@masterno8576]

Ur English is fail

[@masha0242]

You are saving lives sir

[@Haza-rp1cb]

bless you man i got final soon so this is helping me a lot i love you dude

[@mikhelowaabundantmikemomod9540]

Absolutely amazing thanks so much sir

[@MariosMathTutoring]

Most welcome!

[@scottpalmer829]

On # 14, I went from the right with 1/cos - cos/1. Getting a common denominator got me to 1-cos sq. - 1 and then to sin sq./cos. Then I did sin/cos x sin which led to tan /csc. Does this make sense? I know that identities can be done different ways. Hope I got it right. You are great!

[@cosmicnomad8575]

Helpful, because for some reason, I do everything else very well except this

[@summeriswandering628]

omg i wish you were my teacher lol. my teacher is always saying if we need any help or don’t understand something she can work it out to help us but then she gets mad when we ask her to/still don’t understand. also i love the way you wrote all your identities out on the right. we have ours wrote down but my teacher made us write them all over the paper so it’s confusing me so i’m gonna redo them how yours are since my test is tomorrow and i have no clue what i’m doing lol.

[@davidjacob623]

Thank you for the great video Sir! It really helped me.

[@aanyawh0]

I appreciate your help sir.

[@sinsmoth9373]

"most people would have bailed by now- so congrats!" bro ive been trying to learn this for 2 weeeks and my test is tmr, i cannot bail. ty for being nice tho now ima finish this

[@MariosMathTutoring]

Best of luck

[@Haza-rp1cb]

howd it go bro

[@sinsmoth9373]

@@Haza-rp1cb i got a 100 by sheer luck and ended the class w like a 98 😃

[@amirakhoury5507]

This was VERY helpful!!

[@countdowntv366]

This helped so much!! Thank you!!

[@chloexin29]

When would you know to multiply the denominators by the conjugate?

[@Syd034]

I'm lost there too

[@chandanisivakumar4687]

You're the best sir

[@AliHassan-hb1bn]

I loved it. MARIO METHODOLOGY