Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Multiply by $1$ .

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

Step 1.3

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

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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

Step 4

Simplify the expression.

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Step 4.1

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

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

Step 4.2

One to any power is one.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

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

$\sec (x)$