Write the value of (2 ^ -1 1 5 ) - Vidyadip

Question

Write the value of $\tan\Big(2\tan^{-1}\frac{1}{5}\Big)$

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Answer

Let $\tan\theta=\frac{1}{5}$

$\tan\Big(2\tan^{-1}\frac{1}{5}\Big)$

$=\tan2\theta$

$=\frac{2\tan\theta}{1-\tan^2\theta}$

$=\frac{2\times\frac{1}{5}}{1-\frac{1}{25}}$

$=\frac{\frac{2}{5}}{\frac{24}{25}}$

$=\frac{5}{12}$

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