Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

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

Step 5

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

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$1$