Hi, I need help trying figure out this problem: I'm trying to figure out the steps to get from one equation to another

Starting Equation:
Y = X (cos^2Ɵ) (cos^2(π/2 - Ɵ)

**missing steps**

Final Equation:
Y = (X/4) sin^2(2Ɵ)

If anyone can help I'd greatly appreciate it. Thanks!

You need to make use of the fact that \displaystyle \displaystyle \begin{align*} \cos{\left( \frac{\pi}{2} - \theta \right)} \equiv \sin{(\theta)} \end{align*} and \displaystyle \displaystyle \begin{align*} \sin{(2\theta)} \equiv 2\sin{(\theta)}\cos{(\theta)} \end{align*}.

Thanks, but what I really find what's throwing me off is the fact that both the cos are squared in the equation :S

It helps to remember that the product of squares is equal to the square of products...

I'm trying to use the "power reducing" trig identities on this website, but I'm still not getting it...this is driving me crazy
Table of Trigonometric Identities

You are making life difficult on yourself. The only identities you need to use are the ones I gave you. The rest is algebra.