Question 3545
 Do you mean csc x = (cos x)(cot x)
 or 1/sin x = cos x * cos x/sin x 
 or (1- cos^2 x)/sin x = 0,
 or sin^2 x / sin x  = 0
 Since sin x <> 0, we have sin x = 0 (impossible)

 Plz check your typing.
 Whatever the given form is not so important.
 You only need to simplify  
 (cos x)(cot x) = cos^2 x / sin x = (1-sin^2 x)/ sin x
 and then try to solve by yourself.

 Next, use sin (-A) = - sin A and sin(pi - A) = sin A.
 We see that
 sin(x -pi) = sin(-(pi -x)) = - sin(pi-x) = -sin x.

 Kenny