Can someone help me verify this trig identity?
(sin(x))/(1-cos(x))-(sin(x)cos(x))/(1+cos(x))=csc(x)(1+cos^2(x))

O I appluad you on your use of grouping symbols. Few do that when they post a problem.

\frac{sin(x)}{1-cos(x)}-\frac{sin(x)cos(x)}{1+cos(x)}

Cross multiply and simplify:

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

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

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

csc(x)(1+cos^{2}(x))

how did you get (1+cos^2(x)) in the third step?

Factor out the sin(x) in the numerator.