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. 

Your idea is correct. So we have
$$\frac{1}{1-\cos y}+\frac{1}{1+\cos y} = \frac{1+\cos y+ 1-\cos y}{(1+\cos y)(1-\cos y)} = \frac{2}{1-\cos^2 y}.$$
What do you know about $1-\cos^2 y$? Can you take it from here?
