Verifying trig identities specific problem $$\frac1{1-\cos y} + \frac1{1+\cos y} = 2\csc^2y  $$
My attempt was me trying to find a common denominator on the left side but I don't know what to do after that. 

$$\frac{1}{1-\cos y} + \frac1{1+\cos y} =\frac{1}{1-\cos y}\cdot\frac{1+\cos y}{1+\cos y}+\frac{1}{1+\cos y}\cdot\frac{1-\cos y}{1-\cos y}$$$$=\frac{1+\cos y+1-\cos y}{1-\cos^2y}=\frac{2}{1-\cos^2y}=\frac{2}{\sin^2y}=2\csc^2 y$$
