Question

The expression sinx(cscx - cotx cosx) can be simplified to.

Answer 1

Csc x = 1 / sin x  and cot x = cos x/ sin x ;
sin x * ( csc x - cot x * cos x ) =
= sin x * ( 1/sin x - cos x / sin x * cos x ) =
= sin x * ( ( 1 - cos² x ) / sin x ) =
= sin x * ( sin² x / sin x ) =
= sin x * sin x = sin² x   ( answer)