Question

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

• A. $\sqrt{3}-1$
• B. $\pm \sqrt{3}$
• C. $\pm \frac{1}{\sqrt{3}}$
• D. $1-\frac{1}{\sqrt{3}}$

Answer 1

The correct option is C $\pm \frac{1}{\sqrt{3}}$

$cos\left(2ta{n}^{-1}x\right)=\frac{1}{2}$

$\therefore 2ta{n}^{-1}x=co{s}^{-1}\left(\frac{1}{2}\right)$

$\therefore 2ta{n}^{-1}x=\pm \frac{\pi }{3}$

$\therefore ta{n}^{-1}x=\pm \frac{\pi }{6}$

$\therefore x=\pm tan\left(\frac{\pi }{6}\right)$

$\therefore x=\pm \frac{1}{\sqrt{3}}$

Hence, the answer is option (C).