If θ$$=$$$$sin$$−$$1$$⁡$$x+$$$$cos$$−$$1$$⁡x−$$tan$$−$$1$$⁡x≥$$0$$, then the smallest interval in which θ lies, is given by

Correct option is 4π4≤θ≤π2

Questions

$If θ = \sin^{- 1} x + \cos^{- 1} x - \tan^{- 1} x \geq 0,$ then the smallest interval in which $θ$ lies, is given by

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π2≤θ≤3π4

−π4≤θ≤0

0≤θ≤π4

π4≤θ≤π2

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detailed solution

Correct option is D

We have, θ=sin−1⁡x+cos−1⁡x−tan−1⁡x=π2−tan−1⁡x=cot−1⁡xSince, 0≤x≤1, therefore π4≤θ≤π2

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If θ=sin−1⁡x+cos−1⁡x−tan−1⁡x≥0, then the smallest interval in which θ lies, is given by

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Ready to Test Your Skills?

free study material

$If θ = \sin^{- 1} x + \cos^{- 1} x - \tan^{- 1} x \geq 0,$ then the smallest interval in which $θ$ lies, is given by