sin^2 x-4 sin x cos x+3 cos^2 x=0. Created by Kiwiiiiiiiii97. algebra-ru

sin^2 x-4 sin x cos x+3 cos^2 x=0...

July 2022 1 14 Report

sin^2 x-4 sin x cos x+3 cos^2 x=0

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данис2003 Делим на cos² тогда уравнение:
tg²x - 4tgx+3=0
tgx=t
t²-4t+3=0
D=16-4*3=4
t₁=(4-2)/2=1
t₂=(4+2)/2=3
tgx=1
x₁=arctg1+πn, n∈Z
x₁=π/4+πn, n∈Z
x₂=arctg3+πn, n∈Z
Ответ:π/4+πn, arctg3+πn, n∈Z

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