The value of $ sin\left(2 tan^{-1}\frac{1}{3}\right) + cos \left(tan^{-1}2\sqrt{2}\right)$, is
Answer & explanation
Correct answer: option 3
$ sin\left(2 tan^{-1}\frac{1}{3}\right) + cos \left(tan^{-1}2\sqrt{2}\right)$
$=sin \left(sin^{-1}\frac{3}{5}\right) + cos \left(cos^{-1}\frac{1}{3}\right) $ $\left[∵ 2 tan^{-1}x = sin^{-1}\frac{2x}{1+x^2}\right]$
$=\frac{3}{5}+\frac{1}{3}=\frac{14}{15}$