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

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2−1

1-2

π4

3π4

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detailed solution

Correct option is D

Let cot-1(2 -1) = 0⇒ cotθ = 2 -1 Now, cos−1⁡(cos⁡2θ)=cos−1⁡1−tan2⁡θ1+tan2⁡θ =cos−1⁡cot2⁡θ−1cot2⁡θ+1=cos−1⁡2−224−22∴cos−1⁡cos⁡(2θ)=cos−1⁡−12=3π4

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cos−1⁡cos⁡2cot−1⁡(2−1) is equal to

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