Question

Тригонометрия
2sin^2x+2sinx-√3-√3sinx=0

Answer 1

$2\sin^2x+2\sin x-\sqrt{3} -\sqrt{3}\sin x=0 \\\ 2\sin x(\sin x+1)-\sqrt{3} (1+\sin x)=0 \\\ (\sin x+1)(2\sin x-\sqrt{3} )=0$

$\left[\begin{array}{l} \sin x+1=0 \\ 2\sin x-\sqrt{3}=0 \end{array}$

$\left[\begin{array}{l} \sin x=-1 \\ \sin x=\dfrac{\sqrt{3}}{2} \end{array}$

$\left[\begin{array}{l} x_1=-\dfrac{\pi}{2}+2\pi n, \ n\in Z \\ x_2=(-1)^k\cdot \dfrac{\pi}{3}+\pi k, \ k\in Z \end{array}$