Precalculus Examples

$\frac{2}{\sqrt{1 - \cos^{2} (x)}}$

Step 1

Apply pythagorean identity.

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

Step 2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 3

Separate fractions.

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

Step 4

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

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

Step 5

Divide $2$ by $1$ .

$2 \csc (x)$