Question

If $4{\sin }^{-1}x+{\cos }^{-1}x=\pi$, then $x$ is equal to:

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

Answer 1

Answer: (A)

$\frac{1}{2}$

$4{\sin }^{-1}x+{\cos }^{-1}x=\pi$

$\Rightarrow 3{\sin }^{-1}x+({\sin }^{-1}x+{\cos }^{-1}x)=\pi$

$\Rightarrow 3{\sin }^{-1}x+\frac{\pi }{2}=\pi$

$\Rightarrow {\sin }^{-1}x=\frac{\pi }{6}$

$\Rightarrow x=\sin \frac{\pi }{6}=\frac{1}{2}$