Trigonometry Examples

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

Step 1

Rearrange terms.

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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Step 3.1

Multiply by $1$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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

Step 5

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (x)}$ .

$1 \cos (x)$

Step 6

Multiply $\cos (x)$ by $1$ .

$\cos (x)$