Let the function f : 0 , π → ℝ be defined by f θ = sin θ + cos θ 2 + sin θ - cos θ 4 . Suppose the function f has a local minimum at θ precisely when θ ∈ λ 1 π , … , λ r π , where 0 < λ 1 &

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Let the function  f : 0 , &#960; &#8594; &#8477; be defined by  f &#952; = sin &#952; + cos &#952; 2 + sin &#952; - cos &#952; 4 . Suppose the function f has a local minimum at &#952; precisely when  &#952; &#8712; &#955; 1 &#960; , &#8230; , &#955; r &#960; , where 0 &#60; &#955; 1 &#60; &#8943; &#60; &#955; r &#60; 1 . Then the value of   &#955; 1 + &#8943; + &#955; r is_______

Quantrex Academy · Accepted Answer

Correct answer: A. A

f &#952; = 1 + sin 2 &#952; + 1 - sin 2 &#952; 2 = sin 2 2 &#952; - sin 2 &#952; + 2 = sin 2 &#952; - 1 2 2 + 7 4 It has minima when sin 2 &#952; = 1 2 = sin &#960; 6 &#952; &#8712; 0 , &#960; 2 &#952; = &#960; 6 , 5 &#960; 6 &#952; = &#960; 12 , 5 &#960; 12 &#955; 1 = 1 12 , &#160; &#955; 2 = 5 12 sum = 1 2 .

JEE Advanced Mathematics Question (2020) — Solution

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