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Maths-

General

Easy

Question

The value of integer n for which the function $f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction$ has $4 pi$ as its period is

2
3
4
5

hint Hint:

In this question we have to find the value of n in the given function when its period is given. As by fundamental period of period T, f(x+T)=f(x) so using this we can convert f(x) into f(x+T) and later the option which satisfies the equation will be the required value of n.

The correct answer is: 2

$f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction$
Given, period = $4 straight pi$
$s o comma space fraction numerator sin space n straight pi over denominator sin begin display style x over n end style end fraction equals fraction numerator sin open square brackets n open parentheses x plus 4 straight pi close parentheses close square brackets over denominator sin open parentheses begin display style fraction numerator x plus 4 straight pi over denominator n end fraction end style close parentheses end fraction rightwards double arrow fraction numerator sin space n straight pi over denominator sin begin display style x over n end style end fraction equals fraction numerator sin open parentheses n x plus 4 n straight pi close parentheses over denominator sin open parentheses begin display style x over n end style plus begin display style fraction numerator 4 straight pi over denominator n end fraction end style close parentheses end fraction f r o m space o p t i o n s space i t space i s space o n l y space t r u e space f o r space space n equals 2$

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