Maths-
General
Easy

Question

Period of cos to the power of 6 space x plus sin to the power of 6 space x is

  1. pi over 2
  2. pi
  3. fraction numerator 3 pi over denominator 2 end fraction
  4. 2 pi

hintHint:

In this question we have to find the fundamental period oof f(x). As we know, by fundamental property of f(x) periodic function with period T, f(x+T) will be equal to f(x). Now, we will look at the options and check which one will satisfies the statement.

The correct answer is: pi over 2


    By fundamental property of f(x) periodic function with period T.
    f (x+T) =f(x)
    let f (x) =cos to the power of 6 space x plus sin to the power of 6 space x
    assuming from the options smallest period of f(x) to be pi over 2.
    rightwards double arrow f left parenthesis x plus straight pi over 2 right parenthesis equals f left parenthesis x right parenthesis
rightwards double arrow cos to the power of 6 open parentheses x plus straight pi over 2 close parentheses plus sin to the power of 6 open parentheses x plus straight pi over 2 close parentheses equals cos to the power of 6 x plus sin to the power of 6 x
t h e r e f o r e space straight pi over 2 space i s space t h e space f u n d a m e n t a l space p e r i o d space o f space f left parenthesis x right parenthesis.

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