No longer require the answer to this, but if you want to, feel free to try it so I can double check my math (but also my newest question is more urgent).

Prove this identity:

\(1-8sin^2\theta cos^2\theta=cos(4\theta)\)

Prove:

\(1-8sin^2\theta cos^2\theta=cos(4\theta)\\ LHS=1-2(2sin\theta cos\theta)^2\\ LHS=1-2sin^2(2\theta)\\ LHS=1-sin^2(2\theta)-sin^2(2\theta)\\ LHS=cos^2(2\theta)-sin^2(2\theta)\\ LHS=cos(4\theta)\\ LHS=RHS \qquad\\ QED \)