Prove the equation is an identity :
csc3theta - csctheta + cottheta/csctheta = cotsqtheta + costheta
wow ... try that one
Here's where parentheses come in handy.
As written, the identity is wrong. What you meant to say was
(csc^3 - csc + cot)/csc
= (csc(csc^2 - 1) + cot)/csc
= (csc cot^2 + cot)/csc
= csc cot^2/csc + cot/csc
= cot^2 + cos/sin * sin
= cot^2 + cos