Find the Exact Value (tan(pi/18)+tan(pi/9))/(1-tan(pi/18)tan(pi/9))

$\frac{\tan (\frac{π}{18}) + \tan (\frac{π}{9})}{1 - \tan (\frac{π}{18}) \tan (\frac{π}{9})}$

Simplify the numerator.

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Evaluate $\tan (\frac{π}{18})$ .

$\frac{0.17632698 + \tan (\frac{π}{9})}{1 - \tan (\frac{π}{18}) \tan (\frac{π}{9})}$

Evaluate $\tan (\frac{π}{9})$ .

$\frac{0.17632698 + 0.36397023}{1 - \tan (\frac{π}{18}) \tan (\frac{π}{9})}$

Add $0.17632698$ and $0.36397023$ .

$\frac{0.54029721}{1 - \tan (\frac{π}{18}) \tan (\frac{π}{9})}$

Simplify the denominator.

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Evaluate $\tan (\frac{π}{18})$ .

$\frac{0.54029721}{1 - 1 \cdot 0.17632698 \tan (\frac{π}{9})}$

Multiply $- 1$ by $0.17632698$ .

$\frac{0.54029721}{1 - 0.17632698 \tan (\frac{π}{9})}$

Evaluate $\tan (\frac{π}{9})$ .

$\frac{0.54029721}{1 - 0.17632698 \cdot 0.36397023}$

Multiply $- 0.17632698$ by $0.36397023$ .

$\frac{0.54029721}{1 - 0.06417777}$

Subtract $0.06417777$ from $1$ .

$\frac{0.54029721}{0.93582222}$

Divide $0.54029721$ by $0.93582222$ .

$0.57735026$

The result can be shown in multiple forms.

Exact Form:

$\frac{\tan (\frac{π}{18}) + \tan (\frac{π}{9})}{1 - \tan (\frac{π}{18}) \tan (\frac{π}{9})}$

Decimal Form:

$0.57735026 \dots$

Find the Exact Value (tan(pi/18)+tan(pi/9))/(1-tan(pi/18)tan(pi/9))

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