Trigonometry Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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 $b = \sin (x)$ .

$\frac{(1 + \sin (x)) (1 - \sin (x))}{1 - \sin (x)}$

Step 2

Cancel the common factor of $1 - \sin (x)$ .

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Step 2.1

Cancel the common factor.

$\frac{(1 + \sin (x)) (1 - \sin (x))}{1 - \sin (x)}$

Step 2.2

Divide $1 + \sin (x)$ by $1$ .

$1 + \sin (x)$