JEE Advanced | 2013Trigonometric EquationHard

Question

Given A = sin2 θ + cos4 θ then for all real values of θ

Options

A.1 ≤ A ≤ 2
B. ≤ A ≤ 1
C. ≤ A ≤ 1
D. ≤ A ≤

Solution

Given, Asin2 θ + (1 - sin2 θ)2
⇒         Asin4 θ - sin2 θ + 1
⇒        
∵         0 ≤ sin2 θ ≤ 1
⇒        
∴         ≤ A ≤ 1

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