If α≤$$sin$$−$$1$$⁡$$x+$$$$cos$$−$$1$$⁡$$x+$$$$tan$$−$$1$$⁡x≤β, then

Correct option is 1α=π4,β=3π4

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If $α \leq \sin^{- 1} x + \cos^{- 1} x + \tan^{- 1} x \leq β$ , then

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α=π4,β=3π4

α=−π,β=2π

α=0,β=π

none of these

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detailed solution

Correct option is A

We have,sin−1⁡x+cos−1⁡x=π2 for all x∈[−1,1]Also,−π4≤tan⁡x≤π4 for all x∈[−1,1]∴ −π4+π2≤sin−1⁡x+cos−1⁡x+tan−1⁡x≤π4+π2⇒ π4≤sin−1⁡x+cos−1⁡x+tan−1⁡x≤3π4

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If α≤sin−1⁡x+cos−1⁡x+tan−1⁡x≤β, then

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If $α \leq \sin^{- 1} x + \cos^{- 1} x + \tan^{- 1} x \leq β$ , then