Question

find the general solution of the following equation cos 3 X + cos x minus cos 2x is equal to zero​

Answer 1

Answer:

$x = (2n + 1) \frac{\pi}{4} \: \: or \: \: (6n \pm1) \frac{\pi}{3} \: \: where \: n \in \: z$

Explanation

$\cos(3x) + \cos(x) - \cos(2x) = 0 \\ 2 \cos( \frac{3x + x}{2} ) \cos( \frac{3x - x}{2} ) - \cos(2x) = 0\\ \\ 2 \cos(2x) \cos(x) - \cos(2x) = 0 \\ \\ \cos(2x) (2 \cos(x) - 1) = 0 \\\\ \cos(2x) = 0 \: \: \: \: or \: \: \: \: \cos(x) = \frac{1}{2} = \cos( \frac{\pi}{3} ) \\ \\ 2x = \frac{(2n + 1)\pi}{2} \: \: or \: \: x = 2n\pi \pm \frac{\pi}{3}$