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If $α = \sin^{- 1} \frac{\sqrt{3}}{2} + \sin^{- 1} \frac{1}{3}$ and $β = \cos^{- 1} \frac{\sqrt{3}}{2} + \cos^{- 1} \frac{1}{3}$ , then

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α>β

α=β

α<β

α+β=2π

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detailed solution

Correct option is C

From given equations, it can be seen that α+β=πsince sin−1⁡x+cos−1⁡x=π2∀xAlso, α=π3+sin−1⁡13<π3+sin−1⁡12as sinθ is increasing in [0,π2]∴ α<π3+π6=π2⇒β>π2>α⇒α<β

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If α=sin−1⁡32+sin−1⁡13 and β=cos−1⁡32+cos−1⁡13, then

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If $α = \sin^{- 1} \frac{\sqrt{3}}{2} + \sin^{- 1} \frac{1}{3}$ and $β = \cos^{- 1} \frac{\sqrt{3}}{2} + \cos^{- 1} \frac{1}{3}$ , then