Thread:HMcCoy/@comment-25501845-20151002161700/@comment-24808864-20151002180701

That is a great (and challenging) problem. I provided a hint over there, see if it helps!

It uses some strategic "difference of squares" and then applies the identities you mention, but in a creative way.

It should make the gory algebra a little easier to manage.

PS: we usually refer to the cosec(x) as csc(x) so that we maintain the convention of using three letter codes for the trig functions.