Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

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

$\csc (x) \cos (x)$

Step 7

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

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

Step 8

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

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

Step 9

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

$\cot (x)$