Maths-
General
Easy

Question

Period of fraction numerator sin space left parenthesis x plus a right parenthesis over denominator cos space x end fraction

  1. pi over 2
  2. pi
  3. 2 pi
  4. 3 pi

Hint:

In the question we have to find the period of given function. As according to the property of periodic function of the period T, f (x +T) =f (x) So, we will check from the given options which one satisfies the statement.

The correct answer is: pi


    L e t space f left parenthesis x right parenthesis equals fraction numerator sin left parenthesis x plus a right parenthesis over denominator cos space x end fraction
P r o p e r t y space o f space p e r o d i c space f u n c t i o n space o f space p e r i o d space space T
f space left parenthesis x plus T right parenthesis equals f left parenthesis x right parenthesis
B y space p u t t i n g comma space T space equals space straight pi comma space we space get colon
fraction numerator sin space left parenthesis straight pi plus straight x plus straight a right parenthesis over denominator cos space left parenthesis straight pi plus straight x right parenthesis end fraction
equals fraction numerator negative space sin left parenthesis x plus a right parenthesis over denominator negative space cos space x end fraction
equals fraction numerator sin space left parenthesis x plus a right parenthesis over denominator cos space x end fraction
equals f left parenthesis x right parenthesis
S o comma space t h e space p e r i o d space o f space f left parenthesis x right parenthesis space i s space straight pi.

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rightwards double arrow open vertical bar k close vertical bar equals straight pi over 2
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    Maths-General
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    rightwards double arrow fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction equals 4
rightwards double arrow open vertical bar k close vertical bar equals straight pi over 2
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    parallel

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