Trigonometry Examples

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

Start on the right side.

$\sin (x + x)$

Apply the sum of angles identity.

$\sin (x) \cos (x) + \cos (x) \sin (x)$

Simplify the expression.

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Reorder the factors of $\sin (x) \cos (x)$ .

$\cos (x) \sin (x) + \cos (x) \sin (x)$

Add $\cos (x) \sin (x)$ and $\cos (x) \sin (x)$ .

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

Reorder $2 \cos (x)$ and $\sin (x)$ .

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

Reorder $\sin (x)$ and $2$ .

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

Apply the sine double-angle identity.

$\sin (2 x)$

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

$\sin (2 x) = \sin (x + x)$ is an identity