Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Multiply by $1$ .

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

Step 1.3

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

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

Step 2

Apply pythagorean identity.

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

Step 3

Multiply $\sec (x)$ by $\sec^{2} (x)$ by adding the exponents.

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Step 3.1

Multiply $\sec (x)$ by $\sec^{2} (x)$ .

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Step 3.1.1

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

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

Step 3.1.2

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

${\sec (x)}^{1 + 2}$

Step 3.2

Add $1$ and $2$ .

$\sec^{3} (x)$