Prove: $\csc a +\cot a = \cot\frac{a}{2}$ 
Prove: $$\csc a + \cot a = \cot\frac{a}{2}$$

All I have right now, from trig identities, is 
$$\frac{1}{\sin a} + \frac{1}{\tan a} = \frac{1}{\tan(a/2)}$$
Where do I go from there?

Another solution,
$${1\over \sin(a)}= {1\over \tan(a/2)}-{{1-\tan^2(a/2)}\over {2\tan(a/2)}}$$
$${1\over \sin(a)}={1+\tan^2(a/2) \over 2\tan(a/2)}$$
