cos(x+pi/2)=-sinx

Question

to prove the identity above

Answer 1

Sum Formula:

cos(x + π/2)

cos x cos π/2 - sin x sin π/2

cos x (0) - sin x (1)

-sin x

.

Answer 2

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