SinX/1-cosX+sinX/1+cosX

It looks like you're missing some parentheses.

I think this is the equation you mean:

sin (x) / (1-cos (x)) + sin (x) / (1+cos (x))

your common denominator is (1-cos (x)) * (1+cos (x)), which is the difference of squares simplification and is equal to (1-cos^2 (x)) = sin^2 (x)

Numerator: sin (x) * (1+cos (x)) + sin (x) * (1-cos (x))

= sin (x) + sin (x) cos (x) + sin (x) - sin (x) cos (x)

= 2sin (x)

Answer: 2sin (x) / sin^2 (x) = 2/sin (x) = 2csc (x)