Answer
$\cos(x-\frac{\pi}{2})=\sin(x)$
Work Step by Step
$\cos(x-\frac{\pi}{2})$
Expand using subtraction formula for cosine on page 545:
$=\cos(x)\cos(\frac{\pi}{2})+\sin(x)\sin(\frac{\pi}{2})$
Evaluate $\cos(\frac{\pi}{2})$ and $\sin(\frac{\pi}{2})$:
$=\cos(x)*0+\sin(x)*1$
Simplify:
$=\sin(x)$
Therefore, $\cos(x-\frac{\pi}{2})=\sin(x)$.
