Trigonometry Examples

$\sin (2 x) = 2 \cot (x) \sin^{2} (x)$

Step 1

Start on the right side.

$2 \cot (x) \sin^{2} (x)$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $\cot (x)$ in terms of sines and cosines.

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

Step 2.2

Combine $2$ and $\frac{\cos (x)}{\sin (x)}$ .

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

Step 2.3

Cancel the common factor of $\sin (x)$ .

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Step 2.3.1

Factor $\sin (x)$ out of $\sin^{2} (x)$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

Apply the sine double-angle identity.

$\sin (2 x)$

Step 3

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

$\sin (2 x) = 2 \cot (x) \sin^{2} (x)$ is an identity