(sin(x)/(1-cosx))+sinx/(1+cosx)=2cscx
multiply both parts the left hand side by (1+cosx) and (1-cosx) respectively to get:
(sinx(1+cosx))+sinx(1-cosx))/(1-cos^2(x))
Simplify by the pythagorean identity, factoring and basic algebra:
(sin(x)(1+cosx+1-cosx))/(sin^2(x))
2/sin(x)=2cscx
