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Maths-

General

Easy

Question

The period of $fraction numerator sin space left parenthesis 2 pi x plus a right parenthesis over denominator sin space left parenthesis 2 pi x plus b right parenthesis end fraction$ is

$\frac{a}{b}$
1
2
$π$

hint Hint:

In this question, we have to find the period of $fraction numerator sin space left parenthesis 2 pi x plus a right parenthesis over denominator sin space left parenthesis 2 pi x plus b right parenthesis end fraction$ and we know, period of sin kx = $fraction numerator 2 straight pi over denominator 4 end fraction$ . Firstly, we will find the period of the numerator and denominator and using which we can get the required period of function given.

The correct answer is: 1

f(x)= $fraction numerator sin space left parenthesis 2 pi x plus a right parenthesis over denominator sin space left parenthesis 2 pi x plus b right parenthesis end fraction$
Period of sin kx = $fraction numerator 2 straight pi over denominator 4 end fraction$
In numerator,
period of sin ( $2 straight pi plus straight a$ )= $fraction numerator 2 straight pi over denominator 2 straight pi end fraction equals 1$
In denominator,
period of sin ( $2 straight pi plus b$ )= $fraction numerator 2 straight pi over denominator 2 straight pi end fraction equals 1$
So, the period of f(x) is 1.

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