Trigonometry Examples

$2 \tan (2 y)$

Step 1

Apply the tangent double-angle identity.

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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 $b = \tan (y)$ .

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

Step 3

Multiply $2 \frac{2 \tan (y)}{(1 + \tan (y)) (1 - \tan (y))}$ .

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Step 3.1

Combine $2$ and $\frac{2 \tan (y)}{(1 + \tan (y)) (1 - \tan (y))}$ .

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

Step 3.2

Multiply $2$ by $2$ .

$\frac{4 \tan (y)}{(1 + \tan (y)) (1 - \tan (y))}$