Precalculus Examples

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

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

The functions tangent and arctangent are inverses.

$x = x$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $x$ from both sides of the equation.

$x - x = 0$

Step 2.2

Subtract $x$ from $x$ .

$0 = 0$

Step 3

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

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$