Precalculus Examples

$\frac{1}{\sin (x) \cos (x)} - \frac{1}{\tan (x)}$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Write $1$ as a fraction with denominator $1$ .

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

Step 1.4

Simplify.

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Step 1.4.1

Rewrite the expression.

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

Step 1.4.2

Multiply $\frac{\cos (x)}{\sin (x)}$ by $1$ .

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

Step 2

Simplify each term.

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Step 2.1

Separate fractions.

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

Step 2.2

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{1}{\cos (x)} \csc (x) - \frac{\cos (x)}{\sin (x)}$

Step 2.3

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

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

Step 2.4

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

$\sec (x) \csc (x) - \cot (x)$