Let $f(x)=\cos (a x)+\sin (x)$ be periodic. Then $a$ must be

Question

Let $f(x)=\cos (a x)+\sin (x)$ be periodic. Then $a$ must be, Irrational, Rational, Positive real number, Negative real number

MARKS App · Accepted Answer

If function $f(x)=\cos (a x)+\sin (x)$ be periodic, then LCM of $\frac{2 \pi}{|a|}$ and $2 \pi$ must exist and it is only possible if $a$ is a rational number. Hence, option (b) is correct.

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