Precalculus Examples

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

Step 1

Start on the right side.

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

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

$\csc (2 x)$

Step 2.4

Rewrite $\csc (2 x)$ in terms of sines and cosines.

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

Step 3

Rewrite $\frac{1}{\sin (2 x)}$ as $\csc (2 x)$ .

$\csc (2 x)$

Step 4

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

$\csc (2 x) = \frac{1}{2} \cdot (\sec (x) \csc (x))$ is an identity