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