This one you have to know your identities. My professor made me memorize some of the more fundamental ones.
cos(A+B) = cosAcosB – sinAsinB: A = x, B = pi/2, once you plug and chug it's really easy
Therefore, cos (x + pi/2) = cosxcos(pi/2) – sinxsin(pi/2) =
0 - sinx(1) = -sinx