cos^2 x - sin^2 x/ cos^4 x - sin^4 x

Notice the difference of two squares in the num. and den.?.

Remember that x^{2}-y^{2}=(x+y)(x-y)

Actually this whittles down to something very simple.

Remember the identity: cos^{2}(x)-sin^{2}(x)=cos(2x)