# Proving using calculus without trig identity

1. ### kebabs

4
Please I really need help with this hw question

Prove without trig identity that f`(x)=0 for

F(x)=Asin^2(Bx+C)+Acos^2(Bx+C)

2. ### SteveL27

803
You're not supposed to use the obvious identity that simplifies this? I suppose you could just use the derivatives of sin and cos along with the chain rule to directly compute the derivative. But eventually you'll need to simplify using some trig identity.

3. ### kebabs

4
I can't use trig identy to solve it

4. ### kebabs

4
I mean I'm not allowed to

5. ### SammyS

9,265
Staff Emeritus
What is F'(x) if $F(x)=A\sin^2(Bx+C)+A\cos^2(Bx+C)\,?$

6. ### eumyang

1,347
Are you sure? I was able to get F'(x) = 0 by using the chain rule, and yet I didn't use any trig identity.

4

8. ### Ansatz7

29
It's really simple - just use chain rule to take the d/dx of the whole expression. No trig or any other kinds of tricks necessary. Are you familiar with the use of chain rule?

### Staff: Mentor

This is not permitted at Physics Forums - don't even ask.