Question

The domain of $f\left(x\right)=\frac{1}{1-2\sin x}$ is

• A. $(-\infty ,\infty )$
• B. $R-\{n\pi +(-1{)}^n\frac{\pi }{6};n\in Z\}$
• C. $R-\{n\pi :n\in Z\}$
• D. $R-\{n\pi +(-1{)}^n\frac{\pi }{3};n\in z\}$

Answer 1

Answer: (B)

$R-\{n\pi +(-1{)}^n\frac{\pi }{6};n\in Z\}$

$f$ is defined if denominator is not equal to zero

$\Rightarrow 1-2\sin x\ne 0$

$\Rightarrow \sin x\ne \frac{1}{2}$

$\Rightarrow x\ne n\pi +\frac{\pi }{6},\forall n\in Z$

$\therefore$ $f$ is defined for $R-\{n\pi +\frac{\pi }{6}\forall n\in z\}$