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?

Employing Weierstrass half angle relations:
$$\csc a+\cot a=\frac{1+\cos a}{\sin a}=(1+t^2)/2t +(1-t^2)/2t  = 1/t = \cot a/2 .$$
