$\cos5x+\sin4x=0$
$\to \cos5x=-\sin4x=\cos\left(4x+\dfrac{\pi}{2}\right)$
$\to \left[ \begin{array}{l}5x=4x+\dfrac{\pi}{2}+k2\pi \\5x=-4x-\dfrac{\pi}{2}+k2\pi \end{array} \right.$
$\to \left[ \begin{array}{l}x=\dfrac{\pi}{2}+k2\pi \\x=\dfrac{-\pi}{18}+\dfrac{k2\pi}{9}\end{array} \right.$
Nghiệm âm lớn nhất: $\dfrac{-\pi}{18}$
Nghiệm dương nhỏ nhất: $\dfrac{\pi}{2}$