Expand tan(2x)

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Trigonometry

Expand tan(2x)

$\tan (2 x)$

Apply the tangent double-angle identity.

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

Simplify the denominator.

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

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

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 $b = \tan (x)$ .

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

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