Trigonometry Examples

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

Step 1

Apply the sine double-angle identity.

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

Step 2

Cancel the common factor of $\sin (x)$ and $\sin^{2} (x)$ .

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Step 2.1

Factor $\sin (x)$ out of $2 \sin (x) \cos (x)$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Separate fractions.

$\frac{2}{1} \cdot \frac{\cos (x)}{\sin (x)}$

Step 4

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

$\frac{2}{1} \cot (x)$

Step 5

Divide $2$ by $1$ .

$2 \cot (x)$