Let f(x) = | 1 + sin ²x cos ²x sin 2x sin ²x 1 + cos ²x sin 2x sin ²x cos ²x 1 + sin 2x |, x [ (π)/6,(π)/3 ]. If α and β respectively are the maximum and the minimum values of f, then

Sets, Relations and Functions: JEE Main 2023 Mathematics question

JEE Main 2023 · 1 Feb, Morning shift · Q3873

JEE Main 20231 Feb, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let

f(x) = \left| {\matrix{ {1 + {{\sin }^2}x} & {{{\cos }^2}x} & {\sin 2x} \cr {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\sin 2x} \cr {{{\sin }^2}x} & {{{\cos }^2}x} & {1 + \sin 2x} \cr } } \right|,\,x \in \left[ {{\pi \over 6},{\pi \over 3}} \right]

. If

\alpha

and

\beta

respectively are the maximum and the minimum values of

f

, then

JEE Main 2023 · 1 Feb, Morning shift · Q3873

JEE Main 20231 Feb, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let

f(x) = \left| {\matrix{ {1 + {{\sin }^2}x} & {{{\cos }^2}x} & {\sin 2x} \cr {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\sin 2x} \cr {{{\sin }^2}x} & {{{\cos }^2}x} & {1 + \sin 2x} \cr } } \right|,\,x \in \left[ {{\pi \over 6},{\pi \over 3}} \right]

. If

\alpha

and

\beta

respectively are the maximum and the minimum values of

f

, then