Trigonometry Examples

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

Step 1

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

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

Step 2

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (x)}{\cos (x)}$ .

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

Step 3

Write $\cos (x)$ as a fraction with denominator $1$ .

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Simplify the numerator.

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

Add $1$ and $1$ .

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

Step 6

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

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

Step 7

Separate fractions.

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

Step 8

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

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

Step 9

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

$\cos (x) \cot (x)$