Question:

Let a be the smallest positive value of x at which the function f(x) = (cos x^2)(sin x^2) has a critical point. What is the value of f(a)?

The answer begins by using the double angle formula for the sine (sin(2x) = 2sinxcosx) to write the given function in the form f(x) = 1/2 * (sin(2x^2))

I can follow the problem after this point although I do not see how you get the rewritten form. I just need to have that clarified. Thanks.