If the local maximum value of the function f(x)=((√(3 e))/(2 sin x))^ sin ² x, x (0, (π)/2), is k/e, then (k/e)⁸+(k⁸)/(e⁵)+k⁸ is equal to

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 12 Apr, Morning shift · Q2679

JEE Main 202312 Apr, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

If the local maximum value of the function

f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^{2} x}, x \in\left(0, \frac{\pi}{2}\right)

, is

\frac{k}{e}

, then

\left(\frac{k}{e}\right)^{8}+\frac{k^{8}}{e^{5}}+k^{8}

is equal to