Algebra Examples

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

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

Step 1

Simplify the numerator.

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Step 1.1

Rewrite

cot (x)

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

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

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

Step 1.2

Rewrite

tan (x)

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

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

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

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

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

Step 2

Simplify the numerator.

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Step 2.1

Convert from

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

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

tan (x)

$\tan (x)$ .

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

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

Step 2.2

Convert from

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

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

cot (x)

$\cot (x)$ .

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

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

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

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