Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Write $\cos (x)$ as a fraction with denominator $1$ .

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

Divide $\csc (x)$ by $1$ .

$\csc (x) \sin (x)$

Step 8

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 8.1

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

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

Step 8.2

Cancel the common factors.

$1$