Question

Find the domain of 1/1-2 sin x

Answer 1

function is f(x) = 1/(1 - 2sinx)
function is defined only when 1 - 2sinx ≠ 0
Let 1 - 2sinx = 0
sinx = 1/2 = sinπ/3
we know, if sinФ = sinα then, Ф = nπ + (+1)ⁿ α
so, x = nπ + (-1)ⁿπ/3 , where n is integers

Hence, domain of f(x) is all real number except {nπ + (-1)ⁿπ/3}
e.g., domain ∈ R - {nπ + (-1)ⁿπ/3 , n∈I}

Answer 2

Answer:

function is f(x) = 1/(1 - 2sinx)

function is defined only when 1 - 2sinx ≠ 0

Let 1 - 2sinx = 0

sinx = 1/2 = sinπ/3

we know, if sinФ = sinα then, Ф = nπ + (+1)ⁿ α

so, x = nπ + (-1)ⁿπ/3 , where n is integers

Hence, domain of f(x) is all real number except {nπ + (-1)ⁿπ/3}

e.g., domain ∈ R - {nπ + (-1)ⁿπ/3 , n∈I}

Step-by-step explanation: