Question

$co{s}^{-1}\left(cos\right(2co{t}^{-1}(\sqrt{2}-1)\left)\right)$ is equal to

• A. $\sqrt{2}-1$
• B. $\frac{\pi }{4}$
• C. $\frac{3\pi }{4}$
• D. $noneofthese$

Answer 1

The correct option is C $\frac{3\pi }{4}$

$co{s}^{-1}\left(cos\right(2co{t}^{-1}(\sqrt{2}-1)\left)\right)$
$=co{s}^{-1}\left(cos\right({135}^0\left)\right)$
$=co{s}^{-1}\left(\frac{-1}{\sqrt{2}}\right)$
$=\pi -\frac{\pi }{4}$
$=\frac{3\pi }{4}$