First slide

Introduction to ITF

Question

The principal value of $\cos^{- 1} (\cos (2 \cot^{- 1} (\sqrt{2} - 1)))$ is equal to

Easy

A

$\frac{2 π}{3}$
B

$\frac{π}{4}$
C

$\frac{3 π}{4}$
D

$\frac{5 π}{6}$

Solution

$We have, \cos^{- 1} (\cos (2 \cot^{- 1} (\sqrt{2} - 1))) \Rightarrow \cos^{- 1} (\cos (2 \times \frac{3 π}{8})) [∵ \cot \frac{3 π}{8} = \sqrt{2} - 1] \Rightarrow \cos^{- 1} (\cos \frac{3 π}{4}) = \frac{3 π}{4}$

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