Trigonometry Examples

$\sin (3 x) = \sin (2 x + x)$

Step 1

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

$3 x = 2 x + x$

Step 2

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 x + x = 3 x$

Step 3

Add $2 x$ and $x$ .

$3 x = 3 x$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $3 x$ from both sides of the equation.

$3 x - 3 x = 0$

Step 4.2

Subtract $3 x$ from $3 x$ .

$0 = 0$

Step 5

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

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$