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)

$\cos (x)$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Convert from

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

$\csc (x)$ .

$\csc (x)$

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

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