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Functions question

2020 · Shift 2 · Q36

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PYQ Library
JEE Advanced
Mathematics
Functions
2020 · Shift 2 · Q36

Functions question

2020 · Shift 2 · Q36

JEE AdvancedMathematicsFunctionsNumerical+4 / −1

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}\pi \}

, where

0 \lt {\lambda _1} \lt ...{\lambda _r} \lt 1

. Then the value of

{\lambda _1} + ... + {\lambda _r}

is .............

Numerical answer

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