Trigonometry Examples

$1 - \tan^{3} (x)$

Step 1

Rewrite $1$ as $1^{3}$ .

$1^{3} - \tan^{3} (x)$

Step 2

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 1$ and $b = \tan (x)$ .

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

Step 3

Simplify.

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Step 3.1

One to any power is one.

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

Step 3.2

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

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