Verifying Trigonometric Identities Easily - Strategy Explained (14 Examples) 

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!

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!

Love it when teachers do ACTUAL examples Thank you!!

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.

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

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 😎

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

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.

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).

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

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.

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!

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

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

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

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

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

Very thorough and helpful video!

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

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.

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

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

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.

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.

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

Probably the best precalculus on RU-vid! Thank you for these examples !

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

Underrated video

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

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

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

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.

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.

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

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

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

why is this like the most confusing thing I have ever learned. I literally have spent 3 hours on 8 problems and I still can't do them

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

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

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

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! 😁

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

me every time he says positive: ✨PAWSITIVITY✨ then crying during the test

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.

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

This man is a national treasure.

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 !

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

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

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

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

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

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

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:)

You are saving my life right now😭

Ummm ok,, but the fact that he proved it and not us ☺,thanks btw that was so helpful

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

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

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

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

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

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.

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

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!!!

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?

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

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

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.

I'm confused on Problem 2, when you were solving the second step, (1+cos theta)(1-costheta. Like which cosine theta had to camceel out???

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.

got my pre calc quiz tomorrow, I appreciate the review

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

"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

Thank You for teaching me this.

had to leave high school early and get my GED but now trigonometry kickin' my butt in college

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

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

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

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 🇮🇳

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

You're an absolute life-saver!!!

Just a qn, for qn eleven, when multiplying sin square theta over cos theta with cos theta over cos theta should the answer be sin square theta over cos theta

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

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

I genuinely love this guy

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.

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

God bless this man

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

Great for review! Thank you!

You are a great teacher Sir. Mario

About 4 and 11. 4: I have one question. Is it valid to substract one side from both, then just solving numerator = 0? Somehow I was stuck on 4 and I did: csc(x) + cot(x) = sin(x) / (1 - cos(x)) | substituting left side 1 / sin(x) + cos(x) / sin(x) = sin(x) / (1 - cos(x)) | substracting right side from both sides (1 + cos(x)) / sin(x) - sin(x) / (1 - cos(x)) = 0 | combining the fractions by making common denominator (1 - cos^2 - sin^2) / (sin(x) * (1 - cos(x))) = 0 | * (-1) (-1 + 1) / (sin(x) * (1 - cos(x))) = 0 0 = 0 I feel like I remember this being bad practice but I can't remember why. 11: Just another solution. sin(x) * tan(x) / (1 - cos(x)) - 1 = sec(x) | choosing left side and multiplying the first fraction by (1 + cos(x))/(1 + cos(x)) for reciprocal. sin(x) * sin(x)/cos(x) * (1 + cos(x)) / (1 - cos^2(x)) - 1 = sec(x) | 1 - cos^2(x) = sin^2(x) and cancel out 1/cos(x) + 1 - 1 = sec(x) I just wanted to share this one, because for most examples I took a roundabout route, but this one somehow seemed faster. Managed to solve all 14 but took my sweet time. (idk why I did this, trigonometry was a long time ago for me but I guess I wanted a refresher)

You're the best sir

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

Problem 1 is easiest if you start by writing 2 separate fractions. 1 - 1/csc^2 . Then since sine = 1/csc, 1/csc^2 changes to sin^2, so you get 1 - sin^2, which can then be changed to cos^2.

I appreciate your help sir.

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!

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

This helped so much!! Thank you!!

Can you make videos of Integrals