I have to use the derivative definition to determine the derivability of a function at a point. After trying Wolframalpha to help me out, it shows this step, but I don't understand how this:
$$\lim_{h\to 0}\frac{2\cos\left(\frac{\pi+h}{2}\right)\sin\left(\frac{h}{2}\right)}{h}$$ turns into this: $$\lim_{h\to 0}\frac{\cos\left(h\right)-1}{h} $$
I don't recognize a trig identity here. Please explain the magic to me, and help me to solve the limit.