Triginometric Identities

[brandon26]

I have been trying to solve this question for some time but I just cannot find the right solution:

Simplify: 4cosec^2X + (4cosec^2X)(cot^2X)

 

[Fermat]

Take out the common factor.

 

[arildno]

As a follow up to Fermat's suggestion, show that:
$$1+cot^{2}(y)=\frac{1}{\sin^{2}y}$$