Question

Verify 2cotx=csc^2xsin2x

Answer 1

$2\cot x=\csc^2x\sin2x\\\\R=\left(\dfrac{1}{\sin^2x}\right)(2\sin x\cos x)=\dfrac{2\sin x\cos x}{\sin^2x}=\dfrac{2\cos x}{\sin x}=2\left(\dfrac{\cos x}{\sin x}\right)=2\cot x\\\\L=2\cot x\\\\\boxed{L=R}\\\\Used:\\\\\csc x=\dfrac{1}{\sin x}\\\\\cot x=\dfrac{\csc x}{\sin x}$