$1)sinx=-sin9x$
$⇔sinx=sin(-9x)$
$⇔$\(\left[ \begin{array}{l}x=-9x+k2\pi\\x=\pi+9x+k2\pi\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=\dfrac{k\pi}{5}\\x=\dfrac{-\pi}{8}-\dfrac{k\pi}{4}\end{array} \right.\)
$2)sinx=sin(\pi-3x)$
$⇔$\(\left[ \begin{array}{l}x=\pi-3x+k2\pi\\x=\pi-\pi+3x+k2\pi\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}4x=\pi+k2\pi\\-2x=k2\pi\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\x=-k\pi\end{array} \right.\)
$3)sin(-5x)=-sin2x$
$⇔sin(-5x)=sin(-2x)$
$⇔$\(\left[ \begin{array}{l}-5x=-2x+k2\pi\\-5x=\pi+2x+k2\pi\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}-3x=k2\pi\\-7x=\pi+k2\pi\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=\dfrac{-k2\pi}{3}\\x=\dfrac{-\pi}{7}-\dfrac{k2\pi}{7}\end{array} \right.\)
