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Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsProperties of ITFMedium2 minQB

MathematicsMediumsingle choice

Let $I_{1} = π^{2} /16 + 2$ , $I_{2} = (tan^{- 1} (1/ e))^{2} + 2 e / e^{2} + 1$ , $I_{3} = (tan^{- 1} e)^{2} + 2 e / e^{2} + 1$ . Which ordering holds?

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Answer:

Solution:

The printed I₂ has 2e/ $e^{2} + 1$ , not 2/ $e^{2} + 1$ , so the source monotonicity proof does not apply. Direct evaluation gives $I_{2} \approx 2.00128$ , $I_{1} \approx 2.03106$ , $I_{3} \approx 3.36123$ ; hence $I_{2} < I_{1} < I_{3}$ .

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Properties of ITF

⏱ 2mℹ️ Source: QB

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