Giải Pt : cos 4x = -cos 6x

Đáp án:

Giải thích các bước giải:

 `cos\ 4x=-cos\ 6x`

`⇔ cos\ 6x+cos\ 4x=0`

`⇔ 2cos\ \frac{6x+4x}{2} . cos\ \frac{6x-4x}{2}=0`

`⇔ 2cos\ 5x . cos\ x=0`

`⇔` \(\left[ \begin{array}{l}\cos\ 5x=0\\cos\ x=0\end{array} \right.\) 

`⇔` \(\left[ \begin{array}{l}5x=\dfrac{\pi}{2}+k\pi\ (k \in \mathbb{Z})\\x=\dfrac{\pi}{2}+k\pi\ (k \in \mathbb{Z})\end{array} \right.\) 

`⇔` \(\left[ \begin{array}{l}x=\dfrac{\pi}{10}+k\dfrac{\pi}{5}\ (k \in \mathbb{Z})\\x=\dfrac{\pi}{2}+k\pi\ (k \in \mathbb{Z})\end{array} \right.\) 

Vậy `S={\frac{\pi}{10}+k\frac{\pi}{5}\ (k \in \mathbb{Z});\frac{\pi}{2}+k\pi\ (k \in \mathbb{Z})}`