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Question
Find the domain of `1/(1 - 2sinx)`
Solution
Let f(x) = `1/(1 - 2sinx)`
When 1 – 2 sin x = 0
⇒ 1 = 2 sin x
sin x = `1/2`
⇒ sin x = `sin (pi/6)`
x = `"n"pi + (- 1)^"n" pi/6, "n" ∈ "Z"`
sin x = sin α ⇒ x = nπ + (–1)nd, n ∈ Z
∴ Domain of f(x) is `"R" - {"n" pi + (- 1)^"n" pi/6}, "n" ∈ "Z"`
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