однородное тригонометрич уравнение
5sin²x-2sinx × cosx+cos²x=4
5sin^2x-2sinx*cosx+cos^2x=4
5sin^2x-2sinx*cosx+cos^2x - 4= 0 Делим на cos^2x
5tg^2x-2tgx+1 - 4(1+tg^2x) = 0
5tg^2x-2tgx+1-4-4tg^2x=0
tg^2x-2tgx-3=0
D=4+12=16
tgx=3 ->x=arctg 3 +pi*k
tgx=-1 ->x=-pi/4+pi*l
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Answers & Comments
5sin^2x-2sinx*cosx+cos^2x=4
5sin^2x-2sinx*cosx+cos^2x - 4= 0 Делим на cos^2x
5tg^2x-2tgx+1 - 4(1+tg^2x) = 0
5tg^2x-2tgx+1-4-4tg^2x=0
tg^2x-2tgx-3=0
D=4+12=16
tgx=3 ->x=arctg 3 +pi*k
tgx=-1 ->x=-pi/4+pi*l