Trigonometry Examples

$1 - \sin^{4} (x)$

Step 1

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

$1^{2} - \sin^{4} (x)$

Step 2

Rewrite $\sin^{4} (x)$ as ${(\sin^{2} (x))}^{2}$ .

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

Step 3

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 $b = \sin^{2} (x)$ .

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

Factor.

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Step 4.2.1

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 $b = \sin (x)$ .

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

Step 4.2.2

Remove unnecessary parentheses.

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