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
Correct Answer: C
Solution :
Here y would assume real values if \[{{\log }_{3}}cos\{(\sin x)\}\ge 0\]\[\Rightarrow \]\[\cos (\sin x)\ge 1\] \[\Rightarrow \] \[\cos (\sin x)=1\,as-1\le \cos \theta \le 1\] \[\Rightarrow \] \[\sin x=0\] \[\Rightarrow \] \[x=n\pi ,n\in l\] Hence, the domain consists of the multiples of \[\pi \]i.e., domain \[(y)=\{n\pi :n\in l\}.\]
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