Thread: quick question about reciprocal identity

i am dealing with a function involving sqrt x/ csc x. my textbook shows this problem simplifying to (sqrt x sin x). did they use the reciprocal identity? my trig textbook states that sin x= 1/ csc x. is it true to say then that (1)sin x= 1/ csc x? or in this case, sqrt x sin x= sqrt x/ csc x?

By definition, , so is undefined for , . Therefore, for all x and for .