Trigonometry Examples

$(\cot (x) + \tan (x)) \sec (x)$

Step 1

Apply the distributive property.

$\cot (x) \sec (x) + \tan (x) \sec (x)$

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

$\frac{1}{\sin (x)} + \tan (x) \sec (x)$

Step 3

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

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