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JEE Main20202 Sep 2020Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If the equation cos 4 θ + sin 4 θ + λ = 0 has real solutions for θ then λ lies in interval

Options

  1. A- 5 4 , - 1
  2. B- 1 , - 1 2
  3. C- 1 2 , - 1 4
  4. D- 3 2 , - 5 4

Correct answer

B. - 1 , - 1 2

Step-by-step solution

- λ = sin 4 θ + cos 4 θ = sin 2 θ + cos 2 θ 2 - 2 sin 2 θ cos 2 θ = 1 - 4 sin 2 θ cos 2 θ 2 = 1 - sin 2 2 θ 2 ⇒ λ = sin 2 2 θ 2 - 1 λ ∈ - 1 , - 1 2

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