Question

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

Answer 1

prove the identity

Answer 2

what have you tried

Answer 3

i have been looking at all the identities but i dont know where to start

Answer 4

ive tried sum difference identity but idk

Answer 5

I would take right and tried to show the left
I think one of the key identities needed here is :
\[2\cos^2(\theta)-1=\cos(2 \theta)\]

Answer 6

Or ... you could look at the identity
\[1-2\sin^2(\theta)=\cos(2 \theta)\]

Answer 7

\[2-2\sin^2(2x)-2\sin^2(x) \\ =1+1-2\sin^2(2x)-2\sin^2(x) \\= 1-2\sin^2(2x)+1-2\sin^2(x)\]

Answer 8

If I go any further, I would have done the whole problem for you...
Do you think you know where to go from here?

Answer 9

yes

Answer 10

thanks