Question

Помогите решить уравнение
√3+cosx+sinx=0

Answer 1

$\sqrt{3}+Cosx+Sinx=0\\\\Sinx+Sin(\frac{\pi }{2}-x)=-\sqrt{3}\\\\2Sin\frac{x+\frac{\pi }{2}-x }{2}Cos\frac{x-\frac{\pi }{2}+x }{2}=-\sqrt{3}\\\\2Sin\frac{\pi }{4}Cos(x-\frac{\pi }{4})=-\sqrt{3}$

$2*\frac{\sqrt{2} }{2}Cos(x-\frac{\pi }{4})=-\sqrt{3}\\\\\sqrt{2}Cos(x-\frac{\pi }{4})=-\sqrt{3}\\\\Cos(x-\frac{\pi }{4})=-\frac{\sqrt{6} }{2}$

Решений нет, так как - 1 ≤ Cosx ≤ 1