Question

Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`

Answer 1

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}