How do you simplify csc x(sin x + cos x)?

Feb 12, 2016

$1 + \cot x$

Explanation:

Knowing the two identities

$\csc x = \frac{1}{\sin} x \text{ }$ and $\text{ } \cot x = \cos \frac{x}{\sin} x$,

you can simplify as follows:

$\csc x \left(\sin x + \cos x\right) = \frac{1}{\sin} x \left(\sin x + \cos x\right)$

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

$= 1 + \cos \frac{x}{\sin} x$

$= 1 + \cot x$