# How do you simplify sin x + cot x cos x?

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#### Explanation

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#### Explanation:

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22
Jan 26, 2016

$\csc x$

#### Explanation:

We start from the given

$\sin x + \cot x \cos x$

$\sin x + \left(\cos \frac{x}{\sin} x\right) \cdot \cos x$

$\sin x \cdot \left(\sin \frac{x}{\sin} x\right) + \frac{\cos x \cos x}{\sin} x$

because $\sin \frac{x}{\sin} x = 1$, we can always use it in any part of the equation or expression.

fractions having the same denominator can be combined.

it follows

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

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

but ${\sin}^{2} x + {\cos}^{2} x = 1$

therefore

$\frac{1}{\sin} x$

simplifies to

$\csc x$

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