Trigonometry Examples

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

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 $\csc (t)$ and $\tan (t)$ .

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

Step 1.1.2

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

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

Step 1.1.3

Cancel the common factors.

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

Step 1.2

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

$\sec (t) + \sec (- t)$

Step 1.3

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

$\sec (t) + \sec (t)$

Step 2

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

$2 \sec (t)$