Trigonometry Examples

$\frac{\sec (x)}{\tan^{2} (x)}$

Step 1

Factor $\tan (x)$ out of $\tan^{2} (x)$ .

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

Step 2

Separate fractions.

$\frac{1}{\tan (x)} \cdot \frac{\sec (x)}{\tan (x)}$

Step 3

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

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

Step 4

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

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

Step 5

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (x)}{\cos (x)}$ .

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{1}{\tan (x)} \csc (x)$

Step 8

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

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

Step 9

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (x)}{\cos (x)}$ .

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

Step 10

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

$\cot (x) \csc (x)$