Trigonometry Examples

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

Step 1

Start on the right side.

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

Step 2

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

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

Step 3

Simplify.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

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

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

Step 4

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

$\tan (x)$

Step 5

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

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