Precalculus Examples

$\cos (x) + \cos (x) \tan^{2} (x)$

Step 1

Multiply by $1$ .

$\cos (x) \cdot 1 + \cos (x) \tan^{2} (x)$

Step 2

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

$\cos (x) \cdot 1 + \cos (x) (\tan^{2} (x))$

Step 3

Factor $\cos (x)$ out of $\cos (x) \cdot 1 + \cos (x) (\tan^{2} (x))$ .

$\cos (x) \cdot (1 + \tan^{2} (x))$

Step 4

Rearrange terms.

$\cos (x) \cdot (\tan^{2} (x) + 1)$

Step 5

Apply pythagorean identity.

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

Step 6

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

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

Step 7

Simplify the expression.

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Step 7.1

Apply the product rule to $\frac{1}{\cos (x)}$ .

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

Step 7.2

One to any power is one.

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

Step 8

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

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Step 8.1

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

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

Step 8.2

Cancel the common factor.

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

Step 8.3

Rewrite the expression.

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

Step 9

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

$\sec (x)$