JEE Advanced | 2013Trigonometric EquationMedium
Question
Given A = sin2 θ + cos4 θ then for all real values of θ
Options
A.1 ≤ A ≤ 2
B.
≤ A ≤ 1
≤ A ≤ 1C.
≤ A ≤ 1
≤ A ≤ 1D. ≤ A ≤
≤ A ≤ Solution
Given, Asin2 θ + (1 - sin2 θ)2
⇒ Asin4 θ - sin2 θ + 1
⇒
∵ 0 ≤ sin2 θ ≤ 1
⇒
∴
≤ A ≤ 1
⇒ Asin4 θ - sin2 θ + 1
⇒
∵ 0 ≤ sin2 θ ≤ 1
⇒
∴
≤ A ≤ 1Create a free account to view solution
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