I would agree with Drexel28 that the expression on the LHS does not simplify to the RHS. However, is an identity, so far as I can see:
for the LHS.
for the RHS.
A better number is because then you get a zero on the LHS, and there's no way to get a zero on the RHS.
You can simplify the LHS, but not the way they've done. As it turns out, the LHS is zero whenever is even. So substitute to obtain
The last step there you can do because the sin function oscillates between plus and minus one at odd-integer multiples of