0.5×sin2x×ctgx-cosx=sin^2x. Created by LisEhites. matematika-ru

0.5×sin2x×ctgx-cosx=sin^2x...

August 2022 1 1 Report

0.5×sin2x×ctgx-cosx=sin^2x

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yarovoe 0.5sin2x·ctgx-cosx=sin²x
0,5·2sinx·cosx·cosx/sinx-cosx-sin²x=0
cos²x-cosx-(1-cos²x)=cos²x-cosx-1+cos²x=0
2cos²x-cosx-1=0.Пусть cosx=у,тогда имеем: 2у²-у-1=0
D=1²-4·2(-1)=1=8=9,√D=3, y₁=(1+3)/4=1,y₂=(1-3)/4=-0,5
Делаем обратную замену:
cosx=1 и cosx=-0,5
х=2πn,n∈Z x=+-(π-π/3)+2πn=+-2π/3+2πn,
x=+-2π/3+2πn n∈Z

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