How to apply the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles to Sin^2(5x)cos^2(5x)

Question

I need help for my trig class

Answer 1

You know (or should know) that sin²(u)=2sin(u)*cos(u), so sin²(5x)=2sin(5x)*cos(5x)

You also know that cos²(u) =[1+cos(2u)]/2, so cos²(5x) =[1+cos(10x)]/2.

Now sin²(5x)cos²(5x)=2sin(5x)*cos(5x)[1+cos(10x)]/2. Continue from here.