Question

Prove that the left side equals to the right side:

(sin x/(1-cos x))+(sin x/(1+cos x))=2 csc x

(use identities to do that)

Answer 1

LHS,

`= ( \sin(x)(1 + \cos(x)) + \sin(x)(1 - \cos(x) ) )/((1 + \cos(x))(1 - \cos(x)) )`

`= \frac{ \sin(x) + \sin(x) \cos(x) + \sin(x) - \sin(x) \cos(x) }{1 - { (\cos(x)) }^(2) }`

`= \frac{2 \sin(x) }{( { \sin(x) )}^(2) }`

`= (2)/( \sin(x) )`

`= \csc(x)`

hence, proved.