Question

Double angle identity help

Answer 1

Prove whether this is an identity:
cos^2(2x) - sin^2(2x) = 0

To use the double angle identity on this, would I put it to the fourth power?

Answer 2

First of all it's not an identity, it's an equation

Answer 3

cos^2(2x) - sin^2(2x) = cos(4x)=0

Answer 4

I'm supposed to prove whether it's an identity or not... at least, that's what the instructions say

Answer 5

How does it equal cos(4x)?
thanks Faiq :)

Answer 6

If that's the case, reduce to cos(4x) and then state that cos(4x)≠0 for all real values of x

=cos²(2x)-sin²(2x)
=cos²(y)-sin²(y) y=2x
cos(2y)=cos²(y)-sin²(y)
=cos(2y)
=cos(2(2x)) y=2x
=cos(4x)

Answer 7

Give it a counter example to show that it is not an identity, then you are good.
Let say, if x = pi/2, then 2x = pi, right?
cos (pi) = -1 and sin (pit) =0
then you have cos^2 (pi) + sin^2(pi) = 1 \(\neq \) 0
therefore, it is not an identity.

Answer 8

Thank you both!