Question 285481
Since a^2 - b^2 = (a-b)(a+b), apply this with a = cos^2(x) and b = sin^2(x). You have: 
{{{cos^4(x) - sin^4(x)}}} = {{{(cos^2(x) - sin^2(x))(cos^2(x) + sin^2(x))}}} 
Since with every x, sin^2(x) + cos^2(x) = 1, therefore, you can scratch out the factor (cos^2(x) + sin^2(x)). So, cos^4(x) - sin^4(x) = cos^2(x) - sin^2(x).
Is it easy?