Question

y=1/(2 + cosX). Minimum and Maximum values of y

Answer 1

Given $y=\frac{1}{2+\cos x}$. Since $2+\cos x>0$, $y=\frac{1}{2+\cos x}$ is maximum when $2+\cos x$ is minimum and $y=\frac{1}{2+\cos x}$ is minimum when $2+\cos x$ is maximum.

Now,

$\min(2+\cos x)=2-1=1\\ \max(2+\cos x)=2+1=3$

Thus,

The maximum value of $y=\frac{1}{2+\cos x}$ is $1$.

The minimum value of $y=\frac{1}{2+\cos x}$ is $\frac{1}{3}$.