Simplifying Using Trig Identities

Question

Simplify cot(x)/csc(x)-sin(x) to a single trig function. 

Answer 1

cot x / csc x -sin x

=cos x/sinx  / 1/sinx  -sinx............ ( using cotx =cosx/sinx, csc x= 1/sinx)

=cos x/ sinx / 1-sin² x/sinx

=cos x /cos² x...............................( 1-sin² x=cos² x)

=1/cos x