I've tried many times to get the equation to balance using trig identities like half-angle formulas, power-reducing formulas, and double angle formulas, but I couldn't get the equation to equal out. I only need to work one side to make it equal to the other, like a kind of proof. Please help!

Question

1 - 4sin^2(x)cos^2(x) = cos^2(2x)

Answer 1

Can you check your book to see if the given expression is "supposed" to be an identity, or is it a question to solve for x?

The left hand side:
4sin²(x)cos²(x)
=(2sin(x)cos(x))²
=sin²(2x)

Which is not an identity with the right hand side.

If it is an equation, try to solve for x. It would be an excellent exercise.