If f x = 2 tan - 1 x + sin - 1 2 x 1 + x 2 , x > 1 , then f 5 is equal to

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Question: Answered & Verified by Expert

If

f (x) = 2 \tan^{- 1} x + \sin^{- 1} (\frac{2 x}{1 + x^{2}}), x > 1

, then

f (5)

is equal to

MathematicsInverse Trigonometric FunctionsJEE MainJEE Main 2015 (10 Apr Online)

Options:

A $\frac{π}{2}$
B $\tan^{- 1} (\frac{65}{156})$
C $π$
D $4 \tan^{- 1} (5)$

Solution:

1628 Upvotes Verified Answer

The correct answer is:

π

Substitute $\tan^{- 1} x = θ, θ \in (\frac{π}{4}, \frac{π}{2})$

Hence $f (x) = 2 θ + \sin^{- 1} (\sin 2 θ)$

$= 2 θ + π - 2 θ$ , as $(θ > \frac{π}{4})$

$= π$

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