Prove the identity. (must work with left side)

Question

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

Answer 1

Let x^2 = y
What you have written is equivalent to
1 - 2 sin y = cos y
which is not a correct identity.

It looks like you have put parentheses in the wrong places. The outside ones are unecessary.

A correct version would be
1 - 2 (sin x)^2 = cos 2x
That is one of the double-angle identities