<s>[INST] Easy trigonometry question How is
$$\frac{2 \sin x}{(1+ \cos x)^2}= \tan\left(\frac{x}{2}\right)\sec^2\left(\frac{x}{2}\right)\;?$$
It should be easy.
But somehow I don't get it.
Can you help me with this? 
 [/INST] $$\frac{2 \sin x}{(1+ \cos x)^2}=\frac{4 \sin \frac{x}{2}\cos \frac{x}{2}}{(1+ 2\cos^2 \frac{ x}{2}-1)^2}=\frac{ \sin \frac{x}{2}\cos \frac{x}{2}}{( \cos^4 \frac{ x}{2})}=\tan\frac{x}{2}\sec^2\frac{x}{2}$$
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