Question

Let $f\left(x\right)=\sin x+\cos ax$ be periodic function. Then

• A. ${}^{\prime }{a}^{\prime }$ is real number
• B. ${}^{\prime }{a}^{\prime }$ is any irrational number
• C. ${}^{\prime }{a}^{\prime }$ is rational number
• D. $a=0$

Answer 1

The correct option is C ${}^{\prime }{a}^{\prime }$ is rational number

Period of $\sin x+\cos ax$ is LCM of $1$ and $a$.
But for LCM to exist, here ${}^{\prime }{a}^{\prime }$ must be a rational number.