Trigonometry Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

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

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

Step 3

Factor.

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Step 3.1

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

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

Step 3.2

Remove unnecessary parentheses.

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