Question

-2sin(x+n/2)=√2 помогите решить​

Answer 1

$\displaystyle\bf\\-2Sin\Big(x+\frac{\pi }{2} \Big)=\sqrt{2} \\\\\\-2Cosx=\sqrt{2} \\\\\\Cosx=-\frac{\sqrt{2} }{2} \\\\\\x=\pm \ \Big(\pi -arc Cos\frac{\sqrt{2} }{2} \Big)+2\pi n, \ n\in Z\\\\\\x=\pm \ \Big(\pi -\frac{\pi }{4} \Big)+2\pi n, \ n\in Z\\\\\\\boxed{x=\pm \ \frac{3\pi }{4} +2\pi n, \ n\in Z}$