Question

Сполным объяснением! решить уравнение: cos(x/2-пи/8)=0

Answer 1

$cos( \frac{x}{2} - \frac{ \pi }{8} ) = 0 \\ \frac{x}{2} - \frac{ \pi }{8} = \frac{ \pi }{2} + \pi k |*2 \\ x - \frac{ \pi }{4} = \pi + 2\pi k \\ x = \frac{ \pi }{4} + \pi + 2\pi k \\ x = \frac{ 5\pi }{4} + 2\pi k \\ x = - \frac{ 3\pi }{4} + 2\pi k \\$

Answer 2

$cos( \frac{x}{2}- \frac{\pi}{8})=0 \\ \frac{x}{2} - \frac{\pi}{8} = \frac{\pi}{2}+ \pi k \ \ (\cdot 8) \\ 4x-\pi=4\pi +8\pi k \\ 4x = 4\pi+8\pi k + \pi \\ 4x = 5\pi + 8\pi k \\ x = \frac{5\pi}{4} + \frac{8\pi k}{4} \\ x = \frac{5\pi}{4} + 2\pi k \\ \\ \boxed{ k \in Z}$