Question

Решить уравнение sin2x+2cos^2 x=1

Answer 1

$sin2x+2cos^2x=1\2sinxcosx+2cos^2x=sin^2x+cos^2x\sin^2x-2sinxcosx-cos^2x=0|:cos^2x\tg^2x-2tgx-1=0\tgx_{1,2}=1^+_-sqrt{1+1}\tgx_{1,2}=1^+_-sqrt{2}\x_1=arctg(1+sqrt2)+pi n;nin Z\x_2=arctg(1-sqrt2)+pi n;nin Z$