how do I verify that

(csc(x)/ 1 + csc(x)) - (csc(x)/ 1 - csc(x)) = 2 sec ^2(x)

I could use help with this one too, I tried doing it for practice but I am struggling on what to start with, I tried a few things but nothing was working.

\frac{csc(x)}{1+csc(x)}-\frac{csc(x)}{1-csc(x)}

Cross multiply:

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

\frac{-2csc^{2}(x)}{1-csc^{2}(x)}

Note that 1-csc^{2}(x)=-cot^{2}(x)

\frac{2csc^{2}(x)}{cot^{2}(x)}

Now, can you finish? Write it in terms of sin and cos and you should be able to see it?