Question

Verify the identity.

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

Answer 1

cos(4x)=cos(2x+2x)
expand that^

Answer 2

\(\cos4x=1-2\sin^2 2x\)
\(\cos2x=1-2\sin^2x\)
does that help?

Answer 3

It did, but could you please show me how cos 4x = 1 - 2 sin^2 2x?

Answer 4

ya sure.
\(\cos4x=\cos(2x+2x)\)
\(=\cos2x\cos2x-\sin2x\sin2x\)
\(=\cos^2 2x-\sin^2 2x\)
\(=1-\sin^2 2x-\sin^2 2x\) \((\cos^2 2x=1-\sin^2 2x)\)
\(=1-2\sin^2 2x\)

Answer 5

Do you have a reference where it says cos^2 2x = 1−sin^2 2x? I think it would be useful for me since I have a formula sheet but I don't see that on here...

Answer 6

\(\cos^2x+\sin^2x=1\)
Similarly
\(\cos^2 2x+\sin^2 2x=1\)
\(\cos^2 2x=1-\sin^2 2x\)

Answer 7

Thank you for your time and assistance. :)

Answer 8

Welcome:)