Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

$\tan (x) = \tan (x)$

Step 2

For the two functions to be equal, the arguments of each must be equal.

$x = x$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $x$ from both sides of the equation.

$x - x = 0$

Step 3.2

Subtract $x$ from $x$ .

$0 = 0$

Step 4

Since $0 = 0$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$