Trigonometry Examples

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

Step 1

Cancel the common factor of $\cos (x)$ and $\cos^{2} (x)$ .

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Factor $\cos (x)$ out of $2 \cos (x)$ .

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

Cancel the common factors.

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

$\frac{\cos (x) \cdot 2}{\cos (x) \cos (x)}$

Cancel the common factor.

$\frac{\cos (x) \cdot 2}{\cos (x) \cos (x)}$

Rewrite the expression.

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

Step 2

Separate fractions.

$\frac{2}{1} \cdot \frac{1}{\cos (x)}$

Step 3

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

$\frac{2}{1} \sec (x)$

Step 4

Divide $2$ by $1$ .

$2 \sec (x)$