Trigonometry Examples

\frac{\sec (x)}{\tan (x)}

$\frac{\sec (x)}{\tan (x)}$

Step 1

Rewrite

\tan (x)

$\tan (x)$ in terms of sines and cosines.

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

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

Step 2

Rewrite

\sec (x)

$\sec (x)$ in terms of sines and cosines.

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

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

Step 3

Multiply by the reciprocal of the fraction to divide by

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

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

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

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

Step 4

Cancel the common factor of

\cos (x)

$\cos (x)$ .

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Step 4.1

Cancel the common factor.

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

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

Step 4.2

Rewrite the expression.

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

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

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

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

Step 5

Convert from

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

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

\csc (x)

$\csc (x)$ .

\csc (x)

$\csc (x)$