Question

Prove the identity:
[(tanx)/(1-cosx) ] = [(cscx)(1+secx)]

Answer 1

tan x / ( 1 - cos x ) =

`= ( (sinx)/(cosx) )/(1-cos x)= \\ = (sin x)/(( 1 - cos x ) cos x)* (1+cosx)/(1+cos x)= \\ =(sin x(1+cos x))/(sin^(2) xcos x)= \\ =(1+cos x)/(sin x cos x)= (1)/(sin x)* (1+cos x)/(cos x)= \\ =csc x *(1+ (1)/(cos x))=`
= csc x * ( 1 + sec x )
( correct )