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?

$\csc a+\cot a=\cot\frac{a}2$
L.H.S. 
$\implies\large \frac{1}{\sin a}+\frac{\cos a}{\sin a} \\
\implies \large\frac{1+\cos a}{\sin a}\\
\implies \large\frac{1+2\cos^2\frac{a}{2}-1}{\sin a}\\
\implies \large\frac{2\cos^2\frac{a}{2}}{2\sin\frac{a}2\cos\frac{a}{2}}\\
\implies \cot \frac{a}{2}=\text{R.H.S}$
