Question

Complete the identitysin 2x - cot x

Answer 1

Let's complete the identity:

`\begin{gathered} \sin 2x-\cot x=2\sin x\cos x-(\cos x)/(\sin x) \\ =(2\sin^2x\cos x-\cos x)/(\sin x) \\ =(\cos x(2\sin^2x-1))/(\sin x) \\ =(\cos x)/(\sin x)(2\sin ^2x-1) \\ =(\cos x)/(\sin x)(2(1-\cos ^2x)-1) \\ =(\cos x)/(\sin x)(2-2\cos ^2x-1) \\ =(\cos x)/(\sin x)(1-2\cos ^2x) \\ =(\cos x)/(\sin x)(-\cos 2x) \\ =-\cot x\cos 2x \end{gathered}`