Question

6sin^2x+sin2x=2 очень прошу

Answer 1

$sin2x=2sinxcdot cosx\ 6sin^2x+2sinxcdot cosx=2\ 6sin^2x+2sinxcdot cosx-2(sin^2x+cos^2x)=0\ 4sin^2x+2sinxcdot cosx-2cos^2x=0\ frac{4sin^2x+2sinxcdot cosx-2cos^2x}{cos^2x}=0\ 4tg^2x+2tgx-2=0\ 2tg^2x+tgx-1=0\ 2tg^2x+tgx-1=0\ 2tg^2x+2tgx-tgx-1=0\ 2tgx(1+tgx)-(tgx+1)=0\ (2tgx-1)(tgx+1)=0\ tgx_1=0,5\ tgx_2=-1\ x_1=arctg0,5+ pi n\ x_2=- frac{ 3pi }{4} + pi n$