Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Reorder $\csc (x)$ and $\tan (x)$ .

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

Step 1.1.2

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

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

Step 1.1.3

Cancel the common factors.

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

Step 1.2

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

$\sec (x) + \sec (- x)$

Step 1.3

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

$\sec (x) + \sec (x)$

Step 2

Add $\sec (x)$ and $\sec (x)$ .

$2 \sec (x)$