Trigonometry Examples

$\sin (2 x) = 2 \sin (x) \cos (x)$

Step 1

Simplify the right side.

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Step 1.1

Apply the sine double-angle identity.

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

Step 2

Move all terms containing $\sin (2 x)$ to the left side of the equation.

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Step 2.1

Subtract $\sin (2 x)$ from both sides of the equation.

$\sin (2 x) - \sin (2 x) = 0$

Step 2.2

Subtract $\sin (2 x)$ from $\sin (2 x)$ .

$0 = 0$

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:

$(- \infty, \infty)$