Trigonometry Examples

$\frac{6 \tan (x) \cdot (6 \cot (x))}{6 \sec (x)}$

Step 1

Cancel the common factor of $6$ .

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Step 1.1

Cancel the common factor.

$\frac{6 \tan (x) \cdot (6 \cot (x))}{6 \sec (x)}$

Step 1.2

Rewrite the expression.

$\frac{\tan (x) \cdot (6 \cot (x))}{\sec (x)}$

Step 2

Separate fractions.

$\frac{6 \cot (x)}{1} \cdot \frac{\tan (x)}{\sec (x)}$

Step 3

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

$\frac{6 \cot (x)}{1} \cdot \frac{\tan (x)}{\frac{1}{\cos (x)}}$

Step 4

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

$\frac{6 \cot (x)}{1} \cdot \frac{\frac{\sin (x)}{\cos (x)}}{\frac{1}{\cos (x)}}$

Step 5

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

$\frac{6 \cot (x)}{1} (\frac{\sin (x)}{\cos (x)} \cos (x))$

Step 6

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

$\frac{6 \cot (x)}{1} (\frac{\sin (x)}{\cos (x)} \cdot \frac{\cos (x)}{1})$

Step 7

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

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Step 7.1

Cancel the common factor.

$\frac{6 \cot (x)}{1} (\frac{\sin (x)}{\cos (x)} \cdot \frac{\cos (x)}{1})$

Step 7.2

Rewrite the expression.

$\frac{6 \cot (x)}{1} \sin (x)$

Step 8

Divide $6 \cot (x)$ by $1$ .

$6 \cot (x) \sin (x)$

Step 9

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

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Step 9.1

Add parentheses.

$6 (\cot (x) \sin (x))$

Step 9.2

Rewrite $6 \cot (x) \sin (x)$ in terms of sines and cosines.

$6 (\frac{\cos (x)}{\sin (x)} \sin (x))$

Step 9.3

Cancel the common factors.

$6 \cos (x)$