Answer
$x\not=\dfrac{3\pi}{4}+n\pi, n$ is an integer
Work Step by Step
We are given the function:
$f(x)=\dfrac{3}{\sin x+\cos x}$
In order to find the function's domain, we must eliminate the values of $x$ which are solutions of the equation:
$\sin x+\cos x=0$
$(\sin x+\cos x)^2=0$
$\sin^2 x+2\sin x\cos x+\cos^2 x=0$
$(\sin^2 x+\cos^2 x)+\sin (2x)=0$
$1+\sin (2x)=0$
$\sin (2x)=-1$
$2x=\dfrac{3\pi}{2}+2n\pi$
$x=\dfrac{3\pi}{4}+n\pi$
The domain of the function is the set of all real numbers except those in the form $\dfrac{3\pi}{4}+n\pi$, where $n$ is any integer.
