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Question
Find the range of the function `1/(2 cos x - 1)`
Solution
Let f(x) = `1/(2 cos x - 1)`
Range of cosine function is
– 1 ≤ cos x ≤ 1
– 2 ≤ 2 cos x ≤ 2
– 1 ≤ 2 cos x – 1 ≤ 2 – 1
– 3 ≤ 2 cos x – 1 ≤ 1
`- 1/3 ≥ 1/(2 cos x - 1) ≥ 1`
Range of f(x) `[- ∞, (-1)/3] ∪ [1, oo]`
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