Verify the identify csc theta sin theta cot theta cos thet

Verify the identify csc theta - sin theta = cot theta cos theta

Solution

csc theta-sin theta=cot theta costheta

starting with the left side

csc theta - sin theta

csc theta=1/sin theta

1/sin theta - sin theta

(1-sin^2theta)/sin theta

cos^2theta/sin theta= (cos theta/sin theta)cos theta= cot theta cos theta