Verify the identity.

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

Question

Verify the identity.

cos 4x + cos 2x = 2 - 2 sin^2 2x - 2 sin^2 x

anonymous · Answer

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

ajprincess · Answer

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

anonymous · Answer

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

ajprincess · Answer

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

anonymous · Answer

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...

ajprincess · Answer

$\cos^2x+\sin^2x=1$
Similarly
$\cos^2 2x+\sin^2 2x=1$
$\cos^2 2x=1-\sin^2 2x$

anonymous · Answer

Thank you for your time and assistance. :)

ajprincess · Answer

Welcome:)