Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{1}{2 \cos (x)} \csc (x)$

Step 3

Separate fractions.

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

Step 4

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\frac{1}{2} \sec (x) \csc (x)$

Step 5

Simplify with commuting.

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Step 5.1

Reorder $\frac{1}{2} \sec (x)$ and $\csc (x)$ .

$\csc (x) (\frac{1}{2} \sec (x))$

Step 5.2

Reorder $\csc (x)$ and $\frac{1}{2}$ .

$\frac{1}{2} \csc (x) \sec (x)$

$\frac{1}{2} \csc (x) \sec (x)$

Step 6

Combine to $c s c (2 x)$ .

$\csc (2 x)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$