Question

Consider this equation (csc x+1)/cot x = cot x/(csc x +1) is it an identity?

Answer 1

cross multiplying:-
cot^2 x = (csc x+ 1)(csc x + 1)

also cot^2 x = csc^2 x - 1 = (csc x + 1)(csc x - 1) (Known Identitiy)

so the equation is not an identity