Trigonometry Examples

\sin (x) = 2 \sin (\frac{x}{2}) \cos (\frac{x}{2})

$\sin (x) = 2 \sin (\frac{x}{2}) \cos (\frac{x}{2})$

Step 1

Start on the right side.

2 \sin (\frac{x}{2}) \cos (\frac{x}{2})

$2 \sin (\frac{x}{2}) \cos (\frac{x}{2})$

Step 2

Simplify the expression.

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Step 2.1

Apply the sine double-angle identity.

\sin (2 \frac{x}{2})

$\sin (2 \frac{x}{2})$

Step 2.2

Cancel the common factor of

2

$2$ .

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Step 2.2.1

Cancel the common factor.

\sin (2 \frac{x}{2})

$\sin (2 \frac{x}{2})$

Step 2.2.2

Rewrite the expression.

\sin (x)

$\sin (x)$

\sin (x)

$\sin (x)$

\sin (x)

$\sin (x)$

Step 3

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

\sin (x) = 2 \sin (\frac{x}{2}) \cos (\frac{x}{2})

$\sin (x) = 2 \sin (\frac{x}{2}) \cos (\frac{x}{2})$ is an identity