Question

The domain of the function $\sqrt{\frac{1}{\left|\cos x\right|}}$

• A. $R-\left\{\frac{\pi }{2}\right\}$
• B. $R-\left\{\frac{\pi }{2},\frac{3\pi }{2}\right\}$
• C. $R-\left\{\left(2n+1\right)\frac{\pi }{2}:n\in Z\right\}$
• D. $R-\left\{n\pi :n\in Z\right\}$

Answer 1

The correct option is C $R-\left\{\left(2n+1\right)\frac{\pi }{2}:n\in Z\right\}$

$f\left(x\right)=\sqrt{\frac{1}{\left|\cos x\right|}}$

For existance, $\left|\cos x\right|\ne 0$

$x\in R-\left\{\right(2n+1\left)\frac{\pi }{2}\right\}(n\in Z)$