Question

Prove the following identify
Try to solve this

Answer 1

We have to prove that :

$1 + \frac{ { \cot }^{2} \alpha }{1 + \csc\alpha } = \csc\alpha$

On taking L.H.S.

$1 + \frac{ { \cot}^{2} \alpha }{1 + \csc\alpha } \\ \\ = > \frac{1 + \csc\alpha + { \cot }^{2} \alpha }{1 + \csc \alpha } \\ \\ As \: we \: know \: that : \: 1 + { \cot }^{2} \alpha = { \csc }^{2} \alpha \\ \\ = > \frac{1 + \csc\alpha + { \csc }^{2} - 1 }{1 + \csc\alpha } \\ \\ = > \frac{ \csc \alpha + { \csc }^{2} \alpha }{1 + \csc \alpha } \\ \\ = > \frac{ \csc \alpha (1 + \csc \alpha) }{ (1 + \csc\alpha) } \\ \\ = > \csc \alpha = RHS$

HENCE PROVED