Question
Value of $\frac{2\tan^260^\circ}{1+\tan^230^\circ}$ is __________.
✓
Answer
$\frac{2\tan^260^\circ}{1+\tan^230^\circ}\ \dots(1)$
We know that
$\tan60^\circ=\sqrt{3}$
$\tan30^\circ=\frac{1}{\sqrt{3}}$
From eq. (1)
$=\frac{2(\sqrt3)^2}{1+\Big(\frac{1}{\sqrt{3}}\Big)^2}$
$=\frac{2\times3}{1+\Big(\frac{1}{3}\Big)}$
$=\frac{6}{\frac{3+1}{3}}$
$=\frac{6}{\frac{4}{3}}$
$=\frac{18}{4}=\frac{2}{2}$
We know that
$\tan60^\circ=\sqrt{3}$
$\tan30^\circ=\frac{1}{\sqrt{3}}$
From eq. (1)
$=\frac{2(\sqrt3)^2}{1+\Big(\frac{1}{\sqrt{3}}\Big)^2}$
$=\frac{2\times3}{1+\Big(\frac{1}{3}\Big)}$
$=\frac{6}{\frac{3+1}{3}}$
$=\frac{6}{\frac{4}{3}}$
$=\frac{18}{4}=\frac{2}{2}$
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