Let the range of the function \(f\left(x\right)=\frac{1}{2+\sin 3x+\cos 3x},x\in R\) be \([a,b]\). If \(\alpha\) and \(\…

Let the range of the function \(f\left(x\right)=\frac{1}{2+\sin 3x+\cos 3x},x\in R\) be \([a,b]\). If \(\alpha\) and \(\beta\) are respectively the A.M. and the G.M. of a and b, then \(\frac{\alpha }{\beta }\) is equal to

[JEE Main 2024, 9 Apr (Shift 2)]