JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

\tan ^{-1} \frac{2}{p}+\tan ^{-1} \frac{3}{p}+\tan ^{-1} \frac{4}{p}+\tan ^{-1} \frac{5}{p}=\frac{\pi}{2}

, then

\left(p^2+\frac{120}{p^2}\right)

is equal to

View answer and explanation

Correct option: B

Option B (71) is correct because solving the given equation involving inverse tangents leads to the equation

p^4 + 120 = 71p^2

, which directly gives

p^2 + \frac{120}{p^2} = 71

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x

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