Đáp án: 3 họ nghiệm: \(\left[ \begin{array}{l}x=\dfrac{π}{10} +k \dfrac{π}{5}\\x=\dfrac{π}{3}+kπ\\x=\dfrac{-π}{3}+kπ\end{array} \right.\)
Giải thích các bước giải:
`cos7x+ cos5x+cos3x=0`
`<=> (cos7x+cos3x) + cos5x =0`
`<=> 2 cos5x.cos2x + cos5x=0`
`<=> cos5x(2cos2x + 1)=0`
`<=>` \(\left[ \begin{array}{l}cos5x=0\\cos2x=\dfrac{-1}{2}\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}5x=\dfrac{π}{2} +kπ\\cos2x=cos \dfrac{2π}{3}\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\dfrac{π}{10} +k \dfrac{π}{5}\\x=\dfrac{π}{3}+kπ\\x=\dfrac{-π}{3}+kπ\end{array} \right.\)
