Question

Domain of $f(x)=y=\sqrt{{\log }_3\{\cos (\sin x)\}}$ is

• A. $\left\{\frac{n\pi }{2}:n\in l\right\}$
• B. $\{2n\pi :n\in l\}$
• C. $\{n\pi :n\in l\}$
• D. None of the above

Answer 1

Answer: (C)

Here ' $y$ ' would assume real values if
${\log }_3\cos \{(\sin x)\}\ge 0$
$\Rightarrow \cos (\sin x)\ge 1$
$\Rightarrow \cos (\sin x)=1$ as $-1\le \cos \theta \le 1$
$\Rightarrow \sin x=0$
$\Rightarrow x=n\pi ,n\in I$
Hence, the domain consists of the multiples of
$\pi 1.\theta .$ domain $(y)=\{n\pi :n\in /\}$.