Question

What is the value of x that satisfies the equation ${\cos }^{-1}x=2{\sin }^{-1}x$ ?

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

Answer 1

Answer: (A)

Given that ${\cos }^{-1}x=2{\sin }^{-1}x$
$\Rightarrow \frac{\pi }{2}-{\sin }^{-1}x=2{\sin }^{-1}x$
$\Rightarrow \frac{\pi }{2}=3{\sin }^{-1}x$
$\Rightarrow {\sin }^{-1}x=\frac{\pi }{6}$
So, $x=\sin \frac{\pi }{6}=\frac{1}{2}$