How to Prove Trigonometric Identities (and how not to)

[Paul-ebcl]

The students in that class were so fortunate to have Eddie Woo as their teacher. This guy is something else, after just 7 mins I have solved my first Trig identity proof.

[eleliminador]

To be honest, this man is the coolest teacher i have seen in my whole life, youre the best eddie

[Amitsa]

I was feeling sleepy than I switch to your video and all sleep gone, thank you to you and your energy level.

[potatochips]

I wrote the incorrect steps in the exam and got marked wrong for it. I asked my teacher why and she don't give me a reason for it. I had argued with her in front of the class for half the lesson and still don't get why. And here Mr Woo just explains it in literally 2 mins. I thank you so so much for the explanation!

[MrMr]

Imagine actually having a maths 'Teacher'

[shafzkay]

DAMN ur acc so sick. u literally blew my mind with the explanation at the very end

[iglo]

I wish this guy was my math teacher. like the energy and hand gestures and the way how you simplify your explanations so its so easy to understand.... Man thank you so much. Its my first time watching your video and I was hella sleepy, but I felt like I was in the actual classroom when I was watching this video.

[ryiv]

This is exactly how I prove trig. identities even before watching this video. I make an end for both sides through simplification and manipulating identities then makes those ends meet. I learned a lot through this video resurfacing my knowledge about proving trig. identities

[mathematechxblackboard]

Perfect! I have seen this a lot from my students who go to my class with prior knowledge in trigonometry and they present their proofs by starting with the "equation" instead of working from one side to reach the other.

[justshan]

I loved your approach on how to solve complicated Trigonometric Identities.

[ferdousibegum]

U are a total how can anyone explain math like

[DarinBrownSJDCMath]

If each equation is known to be equivalent to the previous one (i.e. you have a string of if and only if's) then there is nothing "wrong" with the first "incorrect" proof you gave. You are simply showing that Equation 1 <==> Equation 2 <==> Equation 3 and since you know Equation 3 is an identity, the first equation must also be an identity. It's a perfectly correct approach to take, provided you understand the reasoning involved. You're not "assuming what you're trying to prove." You're proving that the identity you want to prove is equivalent to a known identity. What you CAN'T do is start with an equation you want to prove is an identity, prove that this equation implies an identity, and then say you've proved the original equation is an identity. For example, you can't start with -3 = 3, square both sides, and say since 9 = 9, we know that -3 = 3 is an identity. That's because the implication only runs in one direction. I would also say it's incorrect to say that an identity is NOT an equation. An identity is simply an equation that is true for all values of the variables under consideration.

[kianwoolston]

I’m in year 9 and I don’t know what any of these symbols means but he just made it so understandable that it seems easy. Great video

[neil_rt]

9 years later and this video is still gold.

[Drforeverok]

Best math teacher ever. Literally never seen a better youtuber who teaches math. Thanks so much

[lukasmoudry]

Except the part when he says you can't do that, which you absolutely can and it is right and there is nothing wrong about it, nice video

[jasonappel]

This is such a good guide. My actual math teacher made me want to jump in front of a train instead of doing the finals.

[morgard]

There is a simillar problem with prove by induction. By plugging in n + 1 into a formula and ending with 0 = 0, you just prove that zero is equal to zero. Exactly as you say, you need to end with n + 1 equivallent of the original formula.

[preciousbees]

2:28 - 55 “I started with this, I can’t start with this I’m supposed to end with this so that can’t be the first line that’s gotta be the last line I’ve got it completely backwards. You’re meant to prove this the burden of proof is in you it’s like walking into a legal court and you’re the defense well everyone assuming THAT my client is innocent... you can’t use that as your basis”

[zac]

I still don't understand why you can't just start with the identity.

If you start with the identity, and then compute the equation (via algebraic manipulation/known theorems) until you reach 0=0, you've effectively proven that the identity is just as true as 0=0. Since 0=0 is clearly true, then so is the identity, and I believe that you have provided sufficient proof. If you were to do this with something that wasn't actually an identity, your final line of working would not reach something that wasn't unequivocally true (i.e. you wouldn't be able to get to 0=0). Therefore this line of working is something that's non-replicable with non-identites, and we can accept it as proof for the given identity.

Can someone please help me understand what is wrong with this line of thinking? Thank you.