Precalculus Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

Tap for more steps...

Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

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

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

Step 7

Combine $\sin (x)$ and $\frac{1}{\cos (x)}$ .

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

Step 8

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

$\tan (x)$