Question

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

Answer 1

@jim_thompson5910 @seiga

Answer 2

@jim_thompson5910

Answer 3

...This is relatively straightforward

Let's work on the RHS . We will use the fact that cos(A+B) = cosAcosB - sinAsinB

Now cos(4x)

= cos(2x + 2x)

= cos(2x)cos(2x) - sin(2x)sin(2x)

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

= LHS, as required