cos^-1 \cos 2 cot^-1(√2-1) \ is equal to

Correct answer: (C) (3 π)/4. cos^-1 [cos \2 · cot^-1(√2-1\ ] . .=cos^-1[cos \2 × 67.5\] ] =cos^-1 [cos 135^° ]=135^°=(3 π)/4

Q101 / 170 · Manipal (MET) 2019 · Mathematics

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

A
$\sqrt{2}-1$
B
$\frac{\pi}{4}$
Correct answer
C
$\frac{3 \pi}{4}$
D
$0$

Solution

$\begin{aligned} & \text { } \cos ^{-1}\left[\cos \left\{2 \cdot \cot ^{-1}(\sqrt{2}-1\}\right]\right. \\ & \left.=\cos ^{-1}[\cos \{2 \times 67.5\}]\right] \\ & =\cos ^{-1}\left[\cos 135^{\circ}\right]=135^{\circ}=\frac{3 \pi}{4}\end{aligned}$

Hence, the correct answer is option: 'C'.

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

Solution

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