Maths-
General
Easy

Question

Period of fraction numerator 2 sin space 2 x minus 5 cos space 2 x over denominator 7 cos space x minus 8 sin space x end fraction is

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

hintHint:

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: 2 pi


    Property of periodic function of period T
    f(x+T)=f(x)
    sinx, cosx are periodic function of period 2straight pi.
    p u t t i n g space T equals 2 straight pi
As comma space fraction numerator 2 sin 2 space open parentheses straight x plus 2 straight pi close parentheses minus 5 cos 2 open parentheses straight x plus 2 straight pi close parentheses over denominator 7 cos open parentheses straight x plus 2 straight pi close parentheses minus 8 sin open parentheses straight x plus 2 straight pi close parentheses end fraction
equals fraction numerator 2 sin 2 straight x minus 5 cos 2 straight x over denominator 7 cosx minus 8 sinx end fraction
equals straight f left parenthesis straight x right parenthesis
So comma space the space period space of space straight f left parenthesis straight x right parenthesis space is space 2 straight pi.

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