Find-the-general-solution-for-the-equation-cos-7x-cos-4x-cos-x-0-

Question Number 157324 by ZiYangLee last updated on 22/Oct/21

Find the general solution for the equation

\cos 7 x - \cos 4 x + \cos x = 0

Commented by cortano last updated on 22/Oct/21

\cos 7 x + \cos x - \cos 4 x = 0

2 \cos 4 x \cos 3 x - \cos 4 x = 0

\cos 4 x (2 \cos 3 x - 1) = 0

{\begin{cases} \cos 4 x = 0 \\ \cos 3 x = \frac{1}{2} \end{cases}

Answered by gsk2684 last updated on 22/Oct/21

\cos 7 x + \cos x - \cos 4 x = 0

2 \cos (\frac{7 x + x}{2}) \cos (\frac{7 x - x}{2}) - \cos 4 x = 0

\cos 4 x (2 \cos 3 x - 1) = 0

\cos 4 x = 0 o r \cos 3 x = \frac{1}{2}

4 x = (2 n + 1) \frac{π}{2} o r 3 x = 2 n π \pm \frac{π}{3} w h e r e n \in I

x = (2 n + 1) \frac{π}{8} o r x = \frac{2 n π}{3} \pm \frac{π}{9} w h e r e n \in I

Facebook Tweet Pin