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The value of $\sin^{- 1} \{\cot (\sin^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos^{- 1} \frac{\sqrt{12}}{4} + \sec^{- 1} \sqrt{2})\}$ , is

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detailed solution

Correct option is C

sin−1⁡cot⁡sin−1⁡2−34+cos−1⁡124+sec−1⁡2=sin−1⁡cot⁡sin−1⁡3−122+cos−1⁡32+sec−1⁡2=sin−1⁡cot⁡π12+π6+π4=sin−1⁡cot⁡π2=sin−1⁡0=0

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The value of sin−1⁡cot⁡sin−1⁡2−34+cos−1⁡124+sec−1⁡2, is

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The value of $\sin^{- 1} \{\cot (\sin^{- 1} \sqrt{\frac{2 - \sqrt{3}}{4}} + \cos^{- 1} \frac{\sqrt{12}}{4} + \sec^{- 1} \sqrt{2})\}$ , is