Solution
For this case we have the following expression:
[tex]\csc ^2x(1+\sin ^2x)=\cot ^2x[/tex]For this case we can do the following:
[tex]\csc ^2x+\csc ^2x\sin ^2x=\frac{1}{\sin^2x}+\frac{1}{\sin^2x}\cdot\sin ^2x=\frac{1}{\sin^2x}+1=\frac{1+\sin ^2x}{\sin ^2x}[/tex]But from this is not possible to show that is equal to cot^2 (x)
So then we can disprove the identity