Question

csc x - sin x = cot x • cos x

Answer 1

1) expand csc and cotx identity 
 
(1/sinx)-sinx = (cosx/sinx)*(cosx)

2) get common denominator on the left side

(1-sin^2x)/(sinx)= (cos^2x)/sinx

3) using cos^2x+sin^2x=1 you finished 
cos^2(x)/sinx= cos^2(x)/sinx

hope that helps