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)\} \geq 0 $
$\Rightarrow \cos (\sin x) \geq 1$
$\Rightarrow \cos (\sin x)=1$ as $-1 \leq \cos \theta \leq 1$
$\Rightarrow \sin x=0$
$\Rightarrow x=n \pi, n \in I$
Hence, the domain consists of the multiples of
$\pi 1 . \theta .$ domain $(y)=\{n \pi: n \in /\}$.