Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

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

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

$\sin (x)$