# Domain of the function $f(x) = \frac{x}{\sqrt{sin(lnx)-cos(lnx)}}$ is

Problem: Domain of the function $\large f(x) = \frac{x}{\sqrt{sin(lnx)-cos(lnx)}}$ is

(A) $( e^{2n\pi} , e^{(3n+1/2)\pi})$

(B) $( e^{(2n+1/4)\pi} , e^{(2n+5/4)\pi})$

(C) $( e^{(2n+1/4)\pi} , e^{(3n-3/4)\pi} )$

(D) none of these

Sol: For domain sin (ln x) > cos (ln x) and x > 0

$2n\pi + \frac{\pi}{4} < lnx < 2n\pi + \frac{5\pi}{4}$ n ∈ I

Hence (B) is the correct answer