Trigonometry Examples

$\sec (- x) \cot (x)$

Step 1

Since $\sec (- x)$ is an even function, rewrite $\sec (- x)$ as $\sec (x)$ .

$\sec (x) \cot (x)$

Step 2

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

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Step 2.1

Reorder $\sec (x)$ and $\cot (x)$ .

$\cot (x) \sec (x)$

Step 2.2

Rewrite $\sec (x) \cot (x)$ in terms of sines and cosines.

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

Step 2.3

Cancel the common factors.

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

Step 3

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc (x)$