# Prove that (sin2x-cos2x)/(sinxcosx)=-cot2x?

Mar 20, 2017

$\frac{{\sin}^{2} x - {\cos}^{2} x}{\sin x \cos x} = - \cot 2 x$

#### Explanation:

I presume you mean

$\frac{{\sin}^{2} x - {\cos}^{2} x}{\sin x \cos x}$

and this can be written as

$- \frac{{\cos}^{2} x - {\sin}^{2} x}{2 \sin x \cos x} \times 2$

= $- \frac{\cos 2 x}{\sin 2 x} \times 2$

= $- 2 \cot 2 x$