Trigonometry Examples

$\csc (x) \sec (x) = \frac{1}{\sin (x) \cos (x)}$

Step 1

Start on the left side.

$\csc (x) \sec (x)$

Step 2

Convert to sines and cosines.

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Step 2.1

Apply the reciprocal identity to $\csc (x)$ .

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

Step 2.2

Apply the reciprocal identity to $\sec (x)$ .

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

Step 3

Multiply $\frac{1}{\sin (x)}$ by $\frac{1}{\cos (x)}$ .

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

Step 4

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

$\csc (x) \sec (x) = \frac{1}{\sin (x) \cos (x)}$ is an identity