First slide

Properties of ITF

Question

If $\cos (2 \tan^{- 1} x) = \frac{1}{2},$ then the value of $x,$ is

Moderate

A

$\sqrt{3}$
B

$\frac{1}{\sqrt{3}}$
C

$1 - \sqrt{3}$
D

$1 - \frac{1}{\sqrt{3}}$

Solution

$\cos (2 \tan^{- 1} x) = \frac{1}{2}$
$\Rightarrow 2 \tan^{- 1} x = \frac{π}{3} \Rightarrow \tan^{- 1} x = \frac{π}{6} \Rightarrow x = \tan \frac{π}{6} = \frac{1}{\sqrt{3}}$

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