Trigonometry Examples

$\tan (- x) \csc (x)$

Step 1

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

$- \tan (x) \csc (x)$

Step 2

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

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Step 2.1

Add parentheses.

$- (\tan (x) \csc (x))$

Step 2.2

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

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

Step 2.3

Cancel the common factors.

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

Step 3

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$- \sec (x)$