QJEEM19Maa0e2: JEE Main 2019 Mathematics - Class 11 JEEM19Maa0e2 Solution: For x ∈ (0, 3/2), let f(x) = x , g(x) = tan x and h(x) = 1 − x…

Question

Verified Solution • 2025–26 Session moderate

For x

\in

(0, 3/2), let f(x) =

\sqrt{x}

, g(x) = tan x and h(x) =

\frac{1 - x^{2}}{1 + x^{2}}

. If

ϕ

(x) = ((hof)og)(x), then

ϕ (\frac{π}{3})

is equal to :

Accepted Answer

ϕ (x) = ((h o f) o g) (x) = h (\sqrt{\tan x})

\Rightarrow ϕ (x) = \frac{1 - \tan x}{1 + \tan x} = \tan (\frac{π}{4} - 4)

∴

ϕ (\frac{π}{3}) = \tan (\frac{π}{4} - \frac{π}{3})

\Rightarrow \tan (- \frac{π}{12}) = \tan \frac{11 π}{12}

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