Question

Find the domain of `1/(1 - 2sinx)`

Answer 1

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"`