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JEE Main20238 Apr 2023Morning ShiftMathematicsDifferentiationActual

Let f x = sin x + cos - 2 sin x - cos x , x ∈ 0 , π - π 4 , then f 7 π 12 f " 7 π 12 is equal to

Options

  1. A2 9
  2. B- 2 3
  3. C- 1 3 3
  4. D2 3 3

Correct answer

A. 2 9

Step-by-step solution

Give that: f x = sin x + cos x - 2 sin x - cos x Convert the numerator and denominator in the form of sin A ± B . ⇒ f x = 2 s in x + π 4 - 2 2 sin x - π 4 ⇒ f x = sin x + π 4 - 1 sin x - π 4 ⇒ f x + π 4 = cos   x - 1 sin   x ⇒ f x + π 4 = - tan x 2 ⇒ f x = - tan x 2 - π 8 ⇒ f ' x = - 1   2 sec 2 x 2 - π 8 ⇒ f " x = - 1 2 sec 2 x 2 - x 8 tan x 2 - π 8 ⇒ f 7 π 12 = - tan 7 π 24 - π 8 = -

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