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

Question

If the equation cos 4 θ + sin 4 θ + λ = 0 has real solutions for θ then λ lies in interval, - 5 4 , - 1, - 1 , - 1 2, - 1 2 , - 1 4, - 3 2 , - 5 4

MARKS App · Accepted Answer

- 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