Question

If $f\left(x\right)=\cos x+\cos ax$ is a periodic function, then '$a$' is necessarily

• A. an integer
• B. a rational number
• C. an irrational number
• D. an even number

Answer 1

The correct option is B a rational number

The function $f\left(x\right)=\cos x+\cos ax$ will be periodic if $a$ is rational.

And the period of the function $f\left(x\right)$ be the LCM of the periods of $\cos x$ and $\cos ax$.

Now $\cos x$ is periodic function of period $2\pi$ and $\cos ax$ is periodic of period $\frac{2\pi }{a}$ for $a$ being rational, for $a\ne 0$.