Trigonometry Examples

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

Step 1

Rearrange terms.

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

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

$\sec (x)$