Prove:

cos(4x) = 1 - 8(sinx)^2(cosx)^2

I have tried and tried and keep ending up with:

(cosx)^4 - 6(cosx)^2(sinx)^2 + (sinx)^4

Here's a hint:

sin^{2}(x)cos^{2}(x)=\frac{1-cos(4x)}{8}

Use the identities:

sin^{2}(x)=\frac{1-cos(2x)}{2}

cos^{2}x=\frac{1+cos(2x)}{2}