Question

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

• A. $\sqrt{2}-1$
• B. $\frac{\pi }{4}$
• C. $\frac{3\pi }{4}$
• D. none of these

Answer 1

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

Given,

${\cos }^{-1}\left(\cos \right(2{\cot }^{-1}(\sqrt{2}-1)\left)\right)$

wkt ${\cot }^{-1}(\sqrt{2}-1)=67.5$

$={\cos }^{-1}\left(\cos \right(2\times 67.5\left)\right)$

$={\cos }^{-1}\left(\cos \right(135)$

$={135}^{\circ }$

$=\frac{3\pi }{4}$