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

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Correct option is C

We have, cos−1⁡cos⁡2cot−1⁡(2−1) ⇒cos−1⁡cos⁡2×3π8 ∵cot⁡3π8=2−1 ⇒cos−1⁡cos⁡3π4=3π4

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The principal value of cos−1⁡cos⁡2cot−1⁡(2−1) is equal to

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