Question

Simplify the trigonometric expression: sin(x) * [csc(x) - sin(x)]
Answer is cos^2(x) but how do you get to that answer

Answer 1

\[\sf \sin(x)[\csc(x)-\sin(x)]\]\[\sin(x)\left[\sf \frac{1}{\sin(x)}-\sin(x)\right]\]multiply in the \(\sin(x)\)\[\sf =1-\sin^2(x)\]use the identity \(\sf sin^2(x) +cos^2(x) = 1\) and you will find your answer.