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JEE Main201912 Apr 2019Morning ShiftMathematicsFunctionsActual

For x ϵ ( 0 , 3 2 ) , let f x = x , g x = t a n x and h x = 1 - x 2 1 + x 2 . If ϕ x = ( h o f ) o g ) ( x ) , then ϕ π 3 is equal to:

Options

  1. Atan ⁡ π 12
  2. Btan ⁡ 5 π 12
  3. Ctan ⁡ 7 π 12
  4. Dtan ⁡ 11 π 12

Correct answer

D. tan ⁡ 11 π 12

Step-by-step solution

f x = x g x = tan x   h x = 1 - x 2 1 + x 2 f o g x = t a n x h o f o g x = h t a n x = 1 - tan x 1 + tan x = tan π 4 - x ϕ x = t a n π 4 - x ϕ π 3 = t a n π 4 - π 3 = tan - π 12 = - tan π 12 = t a n π - π 12 = t a n 11 π 12

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