# How do you verify sin2x * cotx = 1 ?

## sin2x * cotx = 1

Apr 7, 2017

You don't

#### Explanation:

Using the sine double angle formula $\sin \left(2 x\right) = 2 \sin x \cos x$,
$\sin \left(2 x\right) \cdot \cot x = 2 \sin x \cos x \cdot \cot x$.

Knowing that $\cot x = \cos \frac{x}{\sin} x$,
$2 \sin x \cos x \cdot \cot x = 2 \sin x \cos x \cdot \cos \frac{x}{\sin} x$

Simplifying this,
$2 \sin x \cos x \cdot \cos \frac{x}{\sin} x = 2 {\cos}^{2} x$ which does not necessarily equal $1$