20: Sine and cosine are 2π-periodic, so their product is also 2π-periodic, squaring does not change this. Such an answer would not be wrong, however: The squaring flips "lower hills" up, so there is a chance that the basic period gets halved. One can prove that this is true, the given functions is in fact π-periodic. This would also not be a wrong answer. In fact, here we can do one better, the period is actually T = π/2.

One way to guess is to rewrite the given function as

f (x) = [sin(2x)/2]².

The "2x" term divides period by two, the squaring does another halving.

Answer