Question

Решите пожалуйста уравнение cos5x+cosx=0

Answer 1

$\cos5x+\cos x=0$

$2\cos\dfrac{5x+x}{2} \cos\dfrac{5x-x}{2} =0$

$2\cos3x \cos2x =0$

$\left[\begin{array}{l} \cos 3x=0\\ \cos2x=0 \end{array}$

$\left[\begin{array}{l} 3x=\dfrac{\pi}{2}+\pi n \\ 2x=\dfrac{\pi}{2}+\pi n \end{array}$

$\left[\begin{array}{l} x=\dfrac{\pi}{6}+\dfrac{\pi n}{3} \\ x=\dfrac{\pi}{4}+\dfrac{\pi n}{2} \end{array},\ n\in\mathbb{Z}$