How should I have solved this?

So just got my exam and there was this question on it that I just didn't know where to start, wondered if any of you could explain to me how it should have been done.

Had to show that $\displaystyle (cosecx)/(cosecx+1)+(cosecx)/(cosecx-1)=50$ could be written as $\displaystyle sec^2x=25$

I'm pretty sure that was the question, if its not possible then the + is probably a -after the first fraction.

Also the next part was to solve $\displaystyle sec^2x = 25$ and all my friends got 2 answers and I got 4, does that sound right?

Only identies we can use in this exam are

$\displaystyle tan^2x+1=sec^2x$

$\displaystyle cot^2x+1=cosec^2x$

$\displaystyle sin^2x+cos^2x=1$

and all the 1 overs for tan sin and cos.

Thanks!