Question 282257
*[Tex \LARGE \sin(x)(\csc(x)-\sin(x))=\cos^2(x)] ... Start with the given equation.



*[Tex \LARGE \sin(x)\csc(x)-\sin^2(x)=\cos^2(x)] ... Distribute



*[Tex \LARGE \sin(x)\left(\frac{1}{\sin(x)}\right)-\sin^2(x)=\cos^2(x)] ... Replace *[Tex \LARGE \csc(x)] with *[Tex \LARGE \frac{1}{\sin(x)}]



*[Tex \LARGE 1-\sin^2(x)=\cos^2(x)] ... Multiply and simplify.



*[Tex \LARGE \cos^2(x)=\cos^2(x)] ... Use the identity *[Tex \LARGE 1-\sin^2(x)=\cos^2(x)]