Find the range of f(x) = 1/(2cos x−1).

$-1≤ \cos x ≤ 1$

or $-2 ≤ 2 \cos x ≤2$

or $-3≤2 \cos x-1≤1$

For $\frac{1}{2\cos x−1}$,

$-3≤2 \cos x-1<0$ or $0<2\cos x - 1 ≤1$

i.e., $-∞<\frac{1}{2\cos x-1}≤\frac{-1}{3}$ or $1≤\frac{1}{2\cos x- 1}<∞$

Hence, the range is $(-∞,-\frac{1}{3}]∪[1,∞)$