cos7x+cos5x+cos3x=0 giúp mình với

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` 

`<=>` \(\left[ \begin{array}{l}cos5x=0\\cos2x=\dfrac{-1}{2}\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}5x=\dfrac{π}{2} +kπ\\cos2x=cos \dfrac{2π}{3}\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=\dfrac{π}{10} +k \dfrac{π}{5}\\x=\dfrac{π}{3}+kπ\\x=\dfrac{-π}{3}+kπ\end{array} \right.\)