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Question
Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`
Solution
We know the value of cos x lies between –1, 1
–1 ≤ cos x ≤ 1
Multiplying by negative sign, we get
Or 1 ≥ – cos x ≥ –1
Adding 1, we get
2 ≥ 1– cos x ≥ 0 ......(i)
Now, f(x) = `1/sqrt(1 - cos x)`
1– cos x ≠ 0
⇒ cos x ≠ 1
Or, x ≠ 2nπ ∀ n ∈ Z
Therefore, the domain of f = R – {2nπ : n ∈ Z}
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