Please answer the attached question, thank you !!!

Well... what have you attempted so far?

At least in my opinion, this is not a "do your homework for you" forum, so please show some of your work or thought process, be it correct or not.

Anyhow, here are some hints:

(a) If you get stuck at proving identities, you can always try to prove "LHS-RHS=0" instead.

In the solution below, the method of completing square is used, but we're adding/subtracting the middle term instead of the usual last term.

If you've tried the "LHS-RHS=0" approach, you might get an idea why I chose to complete square

(or I've been factoring x^4+y^4 way too many times lately).

(b) Just repeated usage of sinx=cos(pi/2-x).

FULL SOLUTION, STRONGLY ADVICE YOU ATTEMPT THE PROBLEM BEFORE VIEWING

https://www.docdroid.net/4nzV7H4/document-pdf

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Thank you very much for your hints.

Honestly, I and my classmates have tried several times before we decided to post on the forum for help,

we can promise you that we have tried our very best before seeking for help.

Thank you for your advice and hints

原帖由luckjoe於 2021-1-7 07:16 PM 發表

Thank you very much for your hints.

Honestly, I and my classmates have tried several times before we decided to post on the forum for help,

we can promise you that we have tried our very best befo ...

I want to know where you get stuck on so I could give an appropriate response.

Good luck and have fun with math!

a)

LHS

= (cos^2 theta + sin^2 theta)^2 - 2sin^2theta cos^2theta

= 1 - (1/2) (2sin theta cos theta)^2

= 1- (1/2) sin^2 2theta

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