Question

Use the addition formula to derive the identity:

cos(x-pi/2) = sinx

Answer 1

use
\[\cos(\alpha - \beta)=\cos(\alpha)\cos(\beta)+\sin(\alpha)\sin(\beta)\] with
\[\alpha = x, \beta = \frac{\pi}{2}\]

Answer 2

get
\[\cos(x - \frac{\pi}{2})=\cos(x)\cos(\frac{\pi}{2})+\sin(x)\sin(\frac{\pi}{2})\]
and then since
\[\cos(\frac{\pi}{2})=0\] and
\[\sin(\frac{\pi}{2})=1\] you get your result

Answer 3

you're my hero