If the function \(f(x)= \begin{cases}(1+|\cos x|)^ \frac{\lambda}{|\cos x|} & , 0<x<\frac{\pi}{2} \\ \mu &…

If the function \(f(x)= \begin{cases}(1+|\cos x|)^ \frac{\lambda}{|\cos x|} & , 0<x<\frac{\pi}{2} \\ \mu & , \quad x=\frac{\pi}{2} \\ {e^\frac{\cot 6 x}{\cot 4 x}} & \frac{\pi}{2}<x<\pi\end{cases}\)

is continuous at \(x=\frac{\pi}{2}\), then \(9 \lambda+6 \log _e \mu+\mu^6-e^{6 \lambda}\) is equal to

[JEE Main 2023, 25 Jan (Shift 2)]