$y=f(x)=\sin(3x+\pi)+\cot(2x-7x)$
$=-\sin3x+\cot(-5x)$
$=-\sin3x-\cot5x$
ĐK: $\sin5x\ne 0$
$\to 5x\ne k\pi$
$\to x\ne \dfrac{k\pi}{5}$
$\to D=\mathbb{R}$ \ $\left\{ \dfrac{k\pi}{5} \right\}$
Xét $f(-x)=-\sin(-3x)-\cot(-5x)=-(-\sin3x)-(-\cot5x)=\sin3x+\cot5x=-f(x)$
Vậy hàm số lẻ trên $D$