Precalculus Examples

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

Step 1

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

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

Multiply $\frac{\cos (x)}{\sin (x)}$ by $1$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

Add $1$ and $1$ .

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

Step 4.6

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

$\frac{\cos^{2} (x)}{\sin^{1} (x) \sin (x)}$

Step 4.7

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

$\frac{\cos^{2} (x)}{\sin^{1} (x) \sin^{1} (x)}$

Step 4.8

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

$\frac{\cos^{2} (x)}{{\sin (x)}^{1 + 1}}$

Step 4.9

Add $1$ and $1$ .

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

Step 5

Convert from $\frac{\cos^{2} (x)}{\sin^{2} (x)}$ to $\cot^{2} (x)$ .

$\cot^{2} (x)$