Question

Help me? :3
Verify the identity.

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

Answer 1

\[\cos 4x + \cos 2x= 2-2\sin^2 2x - 2\sin^2 x\]

Answer 2

@jdoe0001 @whpalmer4
Okay, I know cos(2x)=1-2sin^2 x, so what does cos 4x equal?

Answer 3

cos(2x + 2x) is one way to do it.

Answer 4

Or cos[2(2x)]

Answer 5

as already pointed out by @KinzaN
\(\bf {\color{blue}{ cos(2\theta)=1-2sin^2(\theta)}}\\ \quad \\ \quad \\

cos(4x) + cos(2x) = 2 - 2 sin^2(2x) - 2 sin^2(x)
\\ \quad \\
\implies cos[2({\color{green}{ 2x}})]+ cos(2x)\implies

{\color{blue}{ 1-2sin^2({\color{green}{ 2x}})}}+{\color{blue}{ 1-2sin^2(x)}}\)

simplify that, see what you get

Answer 6

Oh. I was so close. Dadgummit.