Question

One of the values of x satisfying $\left({\sec }^{-1}x\right)=\sin {\cos }^{-1}\frac{1}{\sqrt{5}}$ is

• A. $\frac{\sqrt{5}}{3}$
• B. $sec\frac{2}{\sqrt{5}}$
• C. $-\frac{\sqrt{5}}{3}$
• D. $-\frac{3}{\sqrt{5}}$

Answer 1

Answer: (B)

$sec\frac{2}{\sqrt{5}}$

$sin\left(co{s}^{-1}\right(\frac{1}{\sqrt{5}}\left)\right)$
$=sin\left(si{n}^{-1}\right(\frac{2}{\sqrt{5}}\left)\right)$
$=\frac{2}{\sqrt{5}}$
$=se{c}^{-1}\left(x\right)$
Hence
$x=sec\left(\frac{2}{\sqrt{5}}\right)$