Question

The value of $θ$ so that ${\sin }^{−1}\left(\frac{2}{\sqrt{5}}\right),{\cos }^{−1}\left(\frac{1}{\sqrt{10}}\right)$ and ${\sin }^{−1}θ$ 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)

${\tan }^{−1}2+{\tan }^{−1}3+{\sin }^{−1}θ=π,⇒{\sin }^{−1}θ+\frac{3π}{4}=π$
$θ=\sin \left(\frac{π}{4}\right)=\frac{1}{\sqrt{2}}$.