Question
The domain of $$f\left( x \right) = \frac{1}{{\sqrt {\left| {\cos \,x} \right| + \cos \,x} }}$$ is :
A.
$$\left[ { - 2n\pi ,\,2n\pi } \right]$$
B.
$$\left( {2n\pi ,\,\overline {2n + 1} \,\pi } \right)$$
C.
$$\left( {\frac{{\left( {4n + 1} \right)\pi }}{2},\,\frac{{\left( {4n + 3} \right)\pi }}{2}} \right)$$
D.
$$\left( {\frac{{\left( {4n - 1} \right)\pi }}{2},\,\frac{{\left( {4n + 1} \right)\pi }}{2}} \right)$$
Answer :
$$\left( {\frac{{\left( {4n - 1} \right)\pi }}{2},\,\frac{{\left( {4n + 1} \right)\pi }}{2}} \right)$$
Solution :
$$\eqalign{
& \left| {\cos \,x} \right| + \cos \,x > 0 \cr
& \Rightarrow \cos \,x > 0 \cr
& \Rightarrow 2n\pi - \frac{\pi }{2} < x < 2n\pi + \frac{\pi }{2} \cr} $$