Question

If ${\cos }^{-1}\left(\frac{1}{\sqrt{5}}\right)=\theta$, then what is the value of $cose{c}^{-1}\left(\sqrt{5}\right)$?

• A. $\left(\frac{\pi }{2}\right)+\theta$
• B. $\left(\frac{\pi }{2}\right)-\theta$
• C. $\left(\frac{\pi }{2}\right)$
• D. $-\theta$

Answer 1

The correct option is B $\left(\frac{\pi }{2}\right)-\theta$

Given,

${\cos }^{-1}\left(\frac{1}{\sqrt{5}}\right)=\theta$

or, $\cos \theta =\frac{1}{\sqrt{5}}$

or, $\sec \theta =\sqrt{5}$

or, $\csc (\frac{\pi }{2}-\theta )=\sqrt{5}$

or, $\frac{\pi }{2}-\theta =cose{c}^{-1}\left(\sqrt{5}\right)$.