Решите уравнение 2sinx*tgx-2tgx-cosx=0

$2sinx* \frac{sinx}{cosx} - \frac{2sinx}{cosx} -cosx=0$

$\frac{2si n^{2}x-2sinx-co s^{2}x }{cosx} =0$

$2si n^{2} x-2sinx-(1-si n^{2} x)=0$

$3si n^{2} x-2sinx-1=0$

Пусть sinx=t;

$3t^{2} -2t-1=0$

D=4+12=16

$t_{1} = \frac{-b- \sqrt{D} }{2a} = \frac{2-4}{6}= -\frac{1}{3}$

$t_{2} = \frac{-b+ \sqrt{D} }{2a} = \frac{2+4}{6} =1$

$sin x_{1} = -\frac{1}{3}$

$x_{1} =arcsin( -\frac{1}{3} )+2pn$ n∈Z

$sin x_{2} = 1$

$x_{2} = \frac{p}{2} +2pn$ n∈Z