Let the function y = (1 − cos x)^(−1), where x ≠ 2nπ and n is an integer. What is the range of the function?

Since cos x ∈ [−1, 1] and x ≠ 2nπ (so cos x ≠ 1), we have 1 − cos x ∈ (0, 2]. Hence y = 1/(1 − cos x) ∈ [1/2, ∞). The minimum value is 1/2 (when cos x = −1) and y can be arbitrarily large as cos x → 1. So range is [0.5, ∞).