Calculus Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

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

$\cos (x) \cos (x)$

Step 7

Multiply $\cos (x) \cos (x)$ .

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Step 7.1

Raise $\cos (x)$ to the power of $1$ .

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

Step 7.2

Raise $\cos (x)$ to the power of $1$ .

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

Step 7.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\cos (x)}^{1 + 1}$

Step 7.4

Add $1$ and $1$ .

$\cos^{2} (x)$