Question

How does cot(x)sin(x)=cos^3(x)+cos(x)sin^2(x)?

Answer 1

$\cot(x)\sin(x)=\cos^3(x)+\cos(x)\sin^2(x)$

$R=\cos(x)[\cos^2(x)+\sin^2(x)]=\cos(x)\cdot1=\cos(x)\\\\L=\dfrac{\cos(x)}{\sin(x)}\cdot\sin(x)=\cos(x)\\\\L=R\\\\\text{used:}\\\\\sin^2x+\cos^2x=1\\\\\cot x=\dfrac{\cos x}{\sin x}$