Let the function f:(0, \\pi) \to{R} be defined by f(\\theta)=(\sin \\theta+\cos \\theta)^{2} +(\sin \\theta-\cos \\theta)^{4} Suppose the function f has a local minimum at \\theta precisely when \\theta\in\{\\lambda_{1} \\pi, ....., \\lambda_{r} \\pit\}, where 0 < \\lambda_ {1} < .......<\λ_{r}<1 .lt;\\lambda_{r}<1 . Then the value of \\lambda_{1}+....+\\lambda_{r} is_______ [JEE Adv 2020 P2]

Functions

Section: Mathematics

Question : 11 of 30

Marks: +1, -0

Let the function f:(0,π)→R be defined by
f(θ)=(sin‌θ+cos‌θ)2 +(sin‌θ−cos‌θ)4
Suppose the function f has a local minimum at θ precisely when θ∈{λ1π,.....,λrπt}, where 0<λ1<.......<λr<1. Then the value of λ1+....+λr is_______

[JEE Adv 2020 P2]

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