Trigonometry Examples

$\sin (8 x) = 2 \sin (4 x) \cos (4 x)$

Step 1

Start on the right side.

$2 \sin (4 x) \cos (4 x)$

Step 2

Simplify the expression.

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Step 2.1

Apply the sine double-angle identity.

$\sin (2 (4 x))$

Step 2.2

Multiply $4$ by $2$ .

$\sin (8 x)$

Step 3

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

$\sin (8 x) = 2 \sin (4 x) \cos (4 x)$ is an identity