Question

Вложение внутри,помогите пожалуйста((

Answer 1

$2sinxcosx-2sinx-cosx+1=0 \\\ 2sinx(cosx-1)-(cosx-1)=0 \\\ (cosx-1)(2sinx-1)=0 \\\ cosx-1=0 \\\ cosx=1 \\\ x=2\pi n, n\in Z \\\ 2sinx-1=0 \\\ sinx=0.5 \\\ x=(-1)^k \frac{\pi}{6} +\pi k, k\in Z$

$2sinx- \sqrt{3} tgx-2 \sqrt{3} cosx+3=0 \\\ 2sinx- \frac{\sqrt{3} sinx}{cosx} -2 \sqrt{3} cosx+ \frac{3cosx}{cosx} =0 \\\ sinx(2- \frac{\sqrt{3} }{cosx})-\sqrt{3}cosx(2 -\frac{\sqrt{3}}{cosx} )=0 \\\ (2- \frac{\sqrt{3} }{cosx})(sinx-\sqrt{3}cosx)=0 \\\ 2- \frac{\sqrt{3} }{cosx}=0 \\\ cosx= \frac{\sqrt{3} }{2} \\\ x=\pm \frac{\pi}{6}+2\pi n, n\in Z \\\ sinx-\sqrt{3}cosx=0 \\\ tgx-\sqrt{3}=0 \\\ tgx=\sqrt{3} \\\ x= \frac{\pi}{3}+\pi n, n\in Z$