Question

sin5x*sin4x + cos6x*cos3x=0​

Answer 1

$sin5x\cdot sin4x+cos6x\cdot cos3x=0\\\frac{1}{2}\left ( cosx-cos9x \right )+\frac{1}{2}\left ( cos3x+cos9x \right )=0\\cosx+cos3x=0\Leftrightarrow 2cos2x\cdot cosx=0\\cos2x=0\Rightarrow x=\frac{\pi}{4}+\frac{\pi k}{2},k\in \mathbb{Z}\\cosx=0\Rightarrow x=\frac{\pi}{2}+\pi k,k\in \mathbb{Z}$