Đáp án:
$\displaystyle S=\left\{\frac{k\pi }{5} ;k\pi ;\frac{\pi }{6} +\frac{k\pi }{3}\right\}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} cos9x-cos7x+cos3x-cosx=0\\ \Leftrightarrow ( cos9x-cosx) -( cos7x-cos3x) =0\\ \Leftrightarrow -2sin5xsin4x+2sin5xsin2x=0\\ \Leftrightarrow 2sin5x( sin2x-sin4x) =0\\ TH1\ sin5x=0\\ \Leftrightarrow 5x=k\pi \ ( k\in \mathbb{Z})\\ \Leftrightarrow x=\frac{k\pi }{5}\\ TH2:\ sin\ 2x=sin4x\\ \Leftrightarrow 4x=2x+k2\pi \ hoặc\ 4x=\pi -2x+k2\pi \\ \Leftrightarrow x=k\pi \ hoặc\ x=\frac{\pi }{6} +\frac{k\pi }{3}\\ Vậy\ S=\left\{\frac{k\pi }{5} ;k\pi ;\frac{\pi }{6} +\frac{k\pi }{3}\right\} \end{array}$
