cot(x) / sec(x) = csc(x) − sin(x)

Question

Verify the identity by converting the left side into sines and cosines. (Simplify at each step.)

Answer 1

left side: cotx/secx = cos(x)/(sinx)/cosx =cos^2(x)/sinx

right side: cscx - sinx= 1/sinx -sin^2(x)/sinx = (1-sin^2(x))/sinx = cos^2(x)/sinx