`cos8x+sin4x=0`
⇔ `1-2sin^{2}4x+sin4x=0`
⇔ `2sin^{2}4x-sin4x-1=0`
⇔ $\left [\begin{array}{l} \sin4x=1 \\ \sin4x=-\dfrac{1}{2} \end{array} \right.$
⇔ $\left [\begin{array}{l} 4x=\dfrac{\pi}{2}+k2π \\ 4x=-\dfrac{\pi}{6}+k2π \\ 4x=\dfrac{7π}{6}+k2π \end{array} \right.$
⇔ $\left [\begin{array}{l} x=\dfrac{\pi}{8}+\dfrac{kπ}{2} \\ x=-\dfrac{\pi}{24}+\dfrac{kπ}{2} \\ x=\dfrac{7π}{24}+\dfrac{kπ}{2} \end{array} \right. \ (k∈\mathbb{Z})$
