Maths-
General
Easy

Question

The domain of the function f left parenthesis x right parenthesis equals square root of cosec space x minus 1 end root text  is  end text

  1. left parenthesis left parenthesis 2 n minus 1 right parenthesis pi comma 2 n pi right parenthesis
  2. left parenthesis 2 n pi comma left parenthesis 2 n plus 1 right parenthesis pi right parenthesis
  3. open parentheses 2 n pi comma 2 n pi plus pi over 2 close square brackets
  4. ϕ

Hint:

In this question, we have to find the domain of f(x). For that for easy calculation we will convert cosec x to 1/sin x. Now as denominator cannot be less than zero, so, the sin x > 0. Thus, using this we can fine the domain of f(x) .

The correct answer is: left parenthesis 2 n pi comma left parenthesis 2 n plus 1 right parenthesis pi right parenthesis


    f left parenthesis x right parenthesis equals square root of cos e c space x minus 1 end root
space space space space space space space equals square root of fraction numerator 1 over denominator sin space x end fraction minus 1 end root
space space space space space space equals square root of fraction numerator 1 minus space sin space x over denominator sin space x end fraction end root
D e m o m i n a t o r space greater than space 0
rightwards double arrow sin x space greater than space 0
rightwards double arrow 2 n straight pi less than straight x less than space left parenthesis 2 straight n plus 1 right parenthesis ππ
So comma space the space domain space of space straight f left parenthesis straight x right parenthesis space is space left parenthesis 2 nπ comma left parenthesis 2 straight n plus 1 right parenthesis straight pi right parenthesis.

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