Find the domain of $f(x)=\sqrt{\cos(\sin x)}$.
Answer & explanation
Correct answer: option 1
$f(x)=\sqrt{\cos(\sin x)}$ is defined if
$\cos(\sin x)≥0$
As we know, $-1 ≤ \sin x ≤ 1$ for all x.
So, $\cos θ≥0$
(Here, $θ= \sin x$ lies in the first and fourth quadrants)
i.e., $\cos (\sin x) ≥ 0$ for all x
i.e., $x ∈ R$
Thus, the domain f(x) is R.