Trigonometry Examples

$\cos (x) (\frac{\sin (x)}{\cos (x)} + \frac{\cos (x)}{\sin (x)})$

Step 1

Simplify each term.

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Step 1.1

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

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

Step 1.2

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

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

Step 2

Apply the distributive property.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

$\frac{\sin (x)}{\cos (x)} \cos (x) + \cos (x) \cot (x)$

Step 3.3

Cancel the common factors.

$\sin (x) + \cos (x) \cot (x)$