Trigonometry Examples

\frac{\cot (x)}{\tan (x)}

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

Step 1

Rewrite

\tan (x)

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

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

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

Step 2

Rewrite

\cot (x)

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

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

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

Step 3

Multiply by the reciprocal of the fraction to divide by

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

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

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

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

Step 4

Simplify.

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Step 4.1

Convert from

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

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

\cot (x)

$\cot (x)$ .

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

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

Step 4.2

Convert from

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

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

\cot (x)

$\cot (x)$ .

\cot (x) \cot (x)

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

Step 4.3

Raise

\cot (x)

$\cot (x)$ to the power of

1

$1$ .

\cot^{1} (x) \cot (x)

$\cot^{1} (x) \cot (x)$

Step 4.4

Raise

\cot (x)

$\cot (x)$ to the power of

1

$1$ .

\cot^{1} (x) \cot^{1} (x)

$\cot^{1} (x) \cot^{1} (x)$

Step 4.5

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

{\cot (x)}^{1 + 1}

${\cot (x)}^{1 + 1}$

Step 4.6

Add

1

$1$ and

1

$1$ .

\cot^{2} (x)

$\cot^{2} (x)$

\cot^{2} (x)

$\cot^{2} (x)$