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

Substitute tan - 1 x = θ , θ ∈ π 4 , π 2 Hence f x = 2 θ + sin - 1 sin 2 θ = 2 θ + π - 2 θ , as θ > π 4 = π

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsGeneral ( General, Domain, Range & Graph)Medium2 minPYQ_2015

MathematicsMediumsingle choice

If $f (x) = 2 \tan^{- 1} x + \sin^{- 1} (\frac{2 x}{1 + x^{2}}), x > 1$ , then $f (5)$ is equal to

Answer:

Solution:

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 $(θ > \frac{π}{4})$

$= π$

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:General ( General, Domain, Range & Graph)

⏱ 2mℹ️ Source: PYQ_2015

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