JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Analyzing +4 | -1

Let

I_1=\frac{\pi^2}{4}+\sqrt{2}, \, \, I_2=\left(\tan ^{-1}\left(\frac{1}{e}\right)\right)^2+\frac{2 e}{\sqrt{e^2+1}}, I_3=\left(\tan ^{-1} e\right)^2+\frac{2}{\sqrt{e^2+1}}

, then which of the following is true?

View answer and explanation

Correct option: B

{I}_2 < {I}_1 < {I}_3

Option B (

{I}_2 < {I}_1 < {I}_3

) is correct because by analyzing the function

f(x)=\left(\tan ^{-1} x\right)^2+\frac{2}{\sqrt{x^2+1}}

and its derivative, we can determine the correct inequality.

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x

{x^2} + {y^2} + {z^2} = {r^2},

{\tan ^{ - 1}}\left( {\frac{{xy}}{{zr}}} \right) + {\tan ^{ - 1}}\left( {\frac{{yz}}{{xr}}} \right) + {\tan ^{ - 1}}\left( {\frac{{xz}}{{yr}}} \right)\;

2{\tan ^{ - 1}}\left( {\frac{1}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right)