Precalculus Examples

$\sin (x) \csc (- x)$

Step 1

Since $\csc (- x)$ is an odd function, rewrite $\csc (- x)$ as $- \csc (x)$ .

$\sin (x) (- \csc (x))$

Step 2

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 2.1

Reorder $\sin (x)$ and $- \csc (x)$ .

$- \csc (x) \sin (x)$

Step 2.2

Add parentheses.

$- (\csc (x) \sin (x))$

Step 2.3

Rewrite $\sin (x) (- \csc (x))$ in terms of sines and cosines.

$- (\frac{1}{\sin (x)} \sin (x))$

Step 2.4

Cancel the common factors.

$- 1 \cdot 1$

Step 3

Multiply $- 1$ by $1$ .

$- 1$