Value of $tan 15^{0}$ equals

2 + \sqrt{3}

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2 - \sqrt{3}

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\sqrt{3} - 2

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\frac{1}{2 - \sqrt{5}}

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Solution

The correct option is B $2 - \sqrt{3}$
$tan 2 (15^{\circ}) = \frac{2 tan 15^{\circ}}{1 - {tan}^{2} 15^{\circ}}$

$tan 15^{\circ} = x$

$\Rightarrow \frac{1}{\sqrt{3}} = \frac{2 x}{1 - x^{2}}$

$\Rightarrow x^{2} + 2 \sqrt{3} x - 1 = 0$

$\Rightarrow x = - \sqrt{3} \pm 2$
Therefore, $t a n 15^{\circ} = 2 - \sqrt{3}$ , because $t a n θ$ is positive for $θ = 15^{0}$

Ans: B

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