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Question

If f(x)=cosx+cosax is a periodic function, then 'a' is necessarily

A
an integer
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B
a rational number
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C
an irrational number
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D
an even number
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Solution

The correct option is B a rational number
The function f(x)=cosx+cosax will be periodic if a is rational.
And the period of the function f(x) be the LCM of the periods of cosx and cosax.
Now cosx is periodic function of period 2π and cosax is periodic of period 2πa for a being rational, for a0.


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