Trigonometry Examples

$\cot (x) \cdot \sec (x) = \csc (x)$

Step 1

Start on the left side.

$\cot (x) \cdot \sec (x)$

Step 2

Convert to sines and cosines.

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Step 2.1

Write $\cot (x)$ in sines and cosines using the quotient identity.

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

Step 2.2

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

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

Step 3

Cancel the common factor of $\cos (x)$ .

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

Step 4

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

$\csc (x)$

Step 5

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

$\cot (x) \cdot \sec (x) = \csc (x)$ is an identity