The simplification of divided difference of cosine function What is the following limit?

$$\lim_{h \to 0}\frac{\cos(\pi/2+h)-\cos(\pi/2)}{h}$$

Why when simplified do you get $(-\sin(h))/h)$?
A cosine wave is just a sine wave shifted to the left by $\frac{\pi}{2}$, so use the following trig identity:

$$\cos(\theta + \frac{\pi}{2}) = \sin(\theta + \frac{\pi}{2} + \frac{\pi}{2}) = \sin(\theta + \pi) = -\sin(\theta)$$
you know :$$cos(a+b)=cos a cos b -sin a sin b\\cos(\frac{\pi}{2}+h)=cos(\frac{\pi}{2})cos h - sin (\frac{\pi}{2}) sin h=0 -1* sin h$$
use this to find that limit 
$$\lim_{h\to 0}\frac{cos(\frac{\pi}{2}+h)-cos \frac{\pi}{2}}{h}=\\\lim_{h\to 0}\frac{-1*sin h-cos \frac{\pi}{2}}{h}=\\\lim_{h\to 0}\frac{-1*sin h-0}{h}$$