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Maths-

General

Easy

Question

If the period of $fraction numerator cos space left parenthesis sin space left parenthesis n x right parenthesis right parenthesis over denominator tan space left parenthesis x divided by n right parenthesis end fraction comma n element of N$ is $6 pi$ then n=

3
2
6
1

hint Hint:

In this question, we have to find the value of n, if period of $fraction numerator cos space left parenthesis sin space left parenthesis n x right parenthesis right parenthesis over denominator tan space left parenthesis x divided by n right parenthesis end fraction comma n element of N$ is $6 pi$ . Firstly, we will find the period of the period of f (x) and then equate it with the period given to get the value of n.

The correct answer is: 3

$L e t space f left parenthesis x right parenthesis space equals space sin space n x space S o comma space g left parenthesis f left parenthesis x right parenthesis right parenthesis equals cos space left parenthesis sin space x right parenthesis space N o w comma space p e r i o d space o f space f left parenthesis x right parenthesis space i s space fraction numerator 2 straight pi over denominator n end fraction S o comma space t h e space p e r i o d space o f space g left parenthesis f left parenthesis x right parenthesis right parenthesis space i s space a l s o space fraction numerator 2 straight pi over denominator n end fraction P e r i o d space o f space d e n o m i n a t o r comma space tan space open parentheses x over n close parentheses space i s space fraction numerator straight pi over denominator begin display style bevelled 1 over n end style end fraction equals n straight pi Given comma space period space is space 6 straight pi Period space of space function space equals fraction numerator LCM thin space of space 2 straight pi space and space nπ over denominator HCF space of space straight n comma space 1 end fraction equals fraction numerator 2 nπ over denominator 1 end fraction Therefore comma space 2 nπ equals space 6 straight pi space rightwards double arrow straight n equals 3$

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