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