Question

The value of $\theta$ so that $\sin ^{-1}\left(\frac{2}{\sqrt{5}}\right), \cos ^{-1}\left(\frac{1}{\sqrt{10}}\right)$ and $\sin ^{-1} \theta$ are the angle of a triangle is

• A. $\frac{-1}{\sqrt{2}}$
• B. $\frac{1}{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

Answer: (C)

$\tan ^{-1} 2+\tan ^{-1} 3+\sin ^{-1} \theta=\pi, \Rightarrow \sin ^{-1} \theta+\frac{3 \pi}{4}=\pi$
$\theta=\sin \left(\frac{\pi}{4}\right)=\frac{1}{\sqrt{2}}$.