The longest period of 4cos3 x - 3cos x is ?

  1. \(\rm \frac {2\pi}{3}\)
  2. \(\rm \frac {\pi}{3}\)
  3. π 
  4. 2π 

Answer (Detailed Solution Below)

Option 1 : \(\rm \frac {2\pi}{3}\)
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Detailed Solution

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Concept:

 Period of a function:
  • If a function repeats over at a constant period we say that is a periodic function.
  • It is represented like f(x) = f(x + T), T is the real number and this is the period of the function.
  • The period of sin x and cos x is 2π

 

Calculation:

To Find: Period of 4cos3 x - 3cos x

As we know 4cos3 x - 3cos x = cos 3x

Period of cos x is 2π

Therefore, the Period of cos 3x is \(\rm \frac {2\pi}{3}\)

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