AP EAMCET · Maths · Functions
Let \(f(x)=\cos (a x)+\sin (x)\) be periodic. Then \(a\) must be
- A Irrational
- B Rational
- C Positive real number
- D Negative real number
Answer & Solution
Correct Answer
(B) Rational
Step-by-step Solution
Detailed explanation
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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