Trigonometry Examples

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

Step 1

Separate fractions.

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

Step 2

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

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

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (x)}$ .

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Add $1$ and $1$ .

$\frac{1}{\sin (x)} \cos^{2} (x)$

Step 5

Combine $\frac{1}{\sin (x)}$ and $\cos^{2} (x)$ .

$\frac{\cos^{2} (x)}{\sin (x)}$

Step 6

Factor $\cos (x)$ out of $\cos^{2} (x)$ .

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

Step 7

Separate fractions.

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

Step 8

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

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

Step 9

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

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