Precalculus Examples

\tan (2 x)

$\tan (2 x)$

Step 1

Apply the tangent double-angle identity.

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

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

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

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

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = 1

$a = 1$ and

b = \tan (x)

$b = \tan (x)$ .

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

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

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

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

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