To solve this trigonometric equation, we can use the trigonometric identity:

sin^2(x) = 1 - cos^2(x)

So, the equation becomes:

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

Using the double angle identity for cosine, we have:

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

Rearranging terms, we get:

cos^2(x) + sin^2(x) = 1

Which is the Pythagorean identity. So, the solution to the equation is all values of x that satisfy the Pythagorean identity.