Trigonometry Examples

$\cot (x) = \frac{1}{\tan (x)}$

Step 1

Start on the right side.

$\frac{1}{\tan (x)}$

Step 2

Write $\tan (x)$ in sines and cosines using the quotient identity.

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

Step 3

Simplify.

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Multiply the numerator by the reciprocal of the denominator.

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

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

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

Step 4

Rewrite $\frac{\cos (x)}{\sin (x)}$ as $\cot (x)$ .

$\cot (x)$

Step 5

Because the two sides have been shown to be equivalent, the equation is an identity.

$\cot (x) = \frac{1}{\tan (x)}$ is an identity