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
- A- 5 4 , - 1
- B- 1 , - 1 2
- C- 1 2 , - 1 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