# Can we prove this is an identity? Sin(x) Cot(x)=Cos(x)

Mar 31, 2018

Yes. See below.

#### Explanation:

It's best to get this in a form involving only sine and cosine.

Recall that $\cot x = \cos \frac{x}{\sin} x$. Applying this to the problem yields:

$\cancel{\sin} x \left(\cos \frac{x}{\cancel{\sin}} x\right) = \cos x$

$\cos x = \cos x$

So, yes, it is an identity.

Mar 31, 2018

#### Explanation:

.

$\sin x \cot x = \cos x$

$\cot x = \cos \frac{x}{\sin} x$

Let's plug it in:

$\sin x \cot x = \sin x \left(\cos \frac{x}{\sin} x\right) = \cancel{\textcolor{red}{\sin}} x \left(\cos \frac{x}{\cancel{\textcolor{red}{\sin}}} x\right)$

$\sin x \cot x = \cos x$