Решить уравнение cos [latex] \frac{x}{2} [/latex]+sin [latex] \frac{x}{2} [/latex]=0

[latex]cos \frac{x}{2} + sin \frac{x}{2} = 0 ; cos \frac{x}{2} \neq 0 =\ \textgreater \ \\ =\ \textgreater \ cos \frac{x}{2} + sin \frac{x}{2} = 0 | :cos \frac{x}{2} \\ 1 + tg\frac{x}{2} = 0 \\ tg\frac{x}{2} = -1 \\ \frac{x}{2} = - \frac{ \pi }{4} + \pi n \\ x = -\frac{\pi}{2} + 2\pi n = \frac{3\pi}{2} + 2\pi n , gde||n||prinadlezhit||z \\ Otvet: \frac{3\pi}{2} + 2\pi n , gde||n||prinadlezhit||z \\[/latex]