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