Question

if tan A = underroot 3 then what is tan 2A​

Answer 1

Answer:

$\tan(a) = \sqrt{3} \\ then \: \tan(2a) = \tan(a + a) = \frac{ 2\tan(a)}{1 - \tan {}^{2} (a)} = \frac{2 \sqrt{3} }{1 - ( \sqrt{3}) {}^{2} } = \frac{2 \sqrt{3} }{(1 - 3)} = \frac{2 \sqrt{3} }{ - 2} = - \sqrt{3}$

Answer 2

$Answer \: \\ \\ \tan(a) = \sqrt{3} \\ \\ \tan(a) = \tan(60) \\ \\ a = 60 \\ \\ so \: \: \: \: \: \: \: \tan(2a) = \tan(2 \times 60) \\ \\ \tan(2a) =</p><p> \tan(120) \\ \\ \tan(120) = \tan(90 + 30) \\ \\ \tan(120) = - \cot(30) \\ \\ \tan(120) = - \sqrt{3} \\ \\ therefore \: \: \tan(2a) = - \sqrt{3} \\ \\ NOTE \\ \: \\ \tan(30) = \frac{1}{ \sqrt{3} } \\ \\ \tan(90 + x) = - \cot(x)$