Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Cancel the common factor of $\cos (x)$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

Step 3

Multiply $\cos (x) \frac{\cos (x)}{\sin (x)}$ .

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Step 3.1

Combine $\cos (x)$ and $\frac{\cos (x)}{\sin (x)}$ .

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

Step 3.2

Raise $\cos (x)$ to the power of $1$ .

$\sin (x) + \frac{\cos^{1} (x) \cos (x)}{\sin (x)}$

Step 3.3

Raise $\cos (x)$ to the power of $1$ .

$\sin (x) + \frac{\cos^{1} (x) \cos^{1} (x)}{\sin (x)}$

Step 3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sin (x) + \frac{{\cos (x)}^{1 + 1}}{\sin (x)}$

Step 3.5

Add $1$ and $1$ .

$\sin (x) + \frac{\cos^{2} (x)}{\sin (x)}$

Step 4

Simplify each term.

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Step 4.1

Factor $\cos (x)$ out of $\cos^{2} (x)$ .

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

Step 4.2

Separate fractions.

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

Step 4.3

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

$\sin (x) + \frac{\cos (x)}{1} \cot (x)$

Step 4.4

Divide $\cos (x)$ by $1$ .

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