For which values of a, f(x)= a(x+sinx) is an increasing function ?

$a≤0$ $a\in (0, ∞)$ $a\in [0, ∞)$ $a \in R$ (set of real numbers)

$a\in [0, ∞)$

The correct answer is Option (3) → $a\in [0, ∞)$ $f(x)= a(x+\sin x)$ $f'(x)=a(1+\cos x)$ (always ≥ 0) as $\cos x∈[-1,1]$ $⇒1+\cos x∈[0,2]$ $⇒a∈[0,∞)$ for $f'(x)≥ 0$