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bart1291
@bart1291
July 2022
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решите уравнение
2sinx*cosx-[tex]cos^{2} [/tex][tex] \frac{x}{2} [/tex]=[tex] sin^{2} [/tex][tex] \frac{x}{2} [/tex]
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Answers & Comments
tfy21075
Cos²(x/2)-sin²(x/2)=cos(2*x/2)=cos(x)
Тогда уравнение принимает вид: 2*sin(x)*cos(x)-cos(x)=0
cos(x)*[2*sin(x)-1]=0
cos(x)=0 и 2*sin(x)-1=0 или sin(x)=1/2
При cos(x)=0 x∈π/2
При sin(x)=1/2 x∈
π/6
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Answers & Comments
Тогда уравнение принимает вид: 2*sin(x)*cos(x)-cos(x)=0
cos(x)*[2*sin(x)-1]=0
cos(x)=0 и 2*sin(x)-1=0 или sin(x)=1/2
При cos(x)=0 x∈π/2
При sin(x)=1/2 x∈π/6