Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

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