Question

The domain of $f\left(x\right)=\text{cosec}x-\cot x$ is

• A. $(-\infty ,\infty )$
• B. $R-\{n\pi$ : $n\in Z\}$
• C. $R-\left\{\right(2n+1)\frac{\pi }{2}$ : $n\in Z\}$
• D. $R-\{\frac{n\pi }{2}:n\in Z\}$

Answer 1

The correct option is B $R-\{n\pi$ : $n\in Z\}$

$\text{cosec}x$ & $\cot x$ are not defined at $x=n\pi \forall n\in Z$
$\therefore$ Domain of $f$ is $R-\left\{n\pi \right\},n\in Z$