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nikith1
@nikith1
July 2022
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50 БАЛЛОВ решить
cos2x=sin3x
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vovochka1997
Sin3x=Cos2x
Sin(2x+x)=Cos2x
Sin2x * Cosx - Cos2x * Sinx = Cos2x
2*Sinx * Cos^2(x) - Cos^2 (x) * Sinx + Sin^3 (x)=Cos2x
Sinx * Cos^2 (x) + Sin^3 (x) = 1-2Sin^2 (x)
Sinx (Cos^2 (x) + Sin^2 (x))=1-2Sin^2 (x)
2Sin^2 (x) + Sinx = 0
Sinx(2Sinx+1) = 0
Sinx=0 или Sinx=-1/2
x=pi*n, n - целое или x=(-1)^(k+1)*pi/6 + pi*k, k - целое
Вот и всё! :)
2 votes
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Answers & Comments
Sin(2x+x)=Cos2x
Sin2x * Cosx - Cos2x * Sinx = Cos2x
2*Sinx * Cos^2(x) - Cos^2 (x) * Sinx + Sin^3 (x)=Cos2x
Sinx * Cos^2 (x) + Sin^3 (x) = 1-2Sin^2 (x)
Sinx (Cos^2 (x) + Sin^2 (x))=1-2Sin^2 (x)
2Sin^2 (x) + Sinx = 0
Sinx(2Sinx+1) = 0
Sinx=0 или Sinx=-1/2
x=pi*n, n - целое или x=(-1)^(k+1)*pi/6 + pi*k, k - целое
Вот и всё! :)