Trigonometry Examples

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

Step 1

Rearrange terms.

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

Step 2

Apply pythagorean identity.

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

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $1$ as $1^{2}$ .

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

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = \tan (x)$ .

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