Trigonometry Examples

$\frac{\cos (x)}{\tan (x) \cot (x)}$

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Multiply $\frac{\sin (x)}{\cos (x)}$ by $\frac{\cos (x)}{\sin (x)}$ .

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

Step 3

Simplify the denominator.

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Step 3.1

Reduce the expression $\frac{\sin (x) \cos (x)}{\cos (x) \sin (x)}$ by cancelling the common factors.

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

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

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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

Step 4

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

$\cos (x)$