Question

The value of $\sin \left(2{\tan }^{-1}\frac{1}{3}\right)+\cos \left({\tan }^{-1}2\sqrt{2}\right)$ is equal to

• A. $\frac{12}{13}$
• B. $\frac{13}{14}$
• C. $\frac{14}{15}$
• D. None of these

Answer 1

The correct option is C $\frac{14}{15}$

Simplifying , we get
$2sin\left(ta{n}^{-1}\left(\frac{1}{3}\right)\right)cos\left(ta{n}^{-1}\left(\frac{1}{3}\right)\right)+co{s}^{-1}\left(cos\left(\frac{1}{3}\right)\right)$
$=2sin\left(si{n}^{-1}\left(\frac{1}{\sqrt{10}}\right)\right)cos\left(co{s}^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)+\frac{1}{3}$
$=\frac{6}{10}+\frac{1}{3}$
$=\frac{3}{5}+\frac{1}{3}$
$=\frac{14}{15}$