Trigonometry Examples

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

Step 1

Apply the distributive property.

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

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 $\cot (x)$ .

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

Step 2.2

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

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

Step 2.3

Cancel the common factors.

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

Step 3

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

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