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линфокс
@линфокс
July 2022
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Решить уравнение sin3x–sin5x=cos4x. 15 баллов
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vishep
Sin3x-sin5x=cos4x
2*cos(3x+5x)/2 * sin(3x-5x)/2=cos 4x
2*cos4x * sin(-x)=cos 4x
2*cos4x * sin(-x) - cos 4x = 0
cos4x * (2*sin(-x) - 1) = 0
два решения
cos4x=0 4 x = Pi/2 + kPi x = Pi/8 + kPi/4
sin(x) = -1/2
x = (-1)^(n+1)Pi/6 + nPi
2 votes
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Answers & Comments
2*cos(3x+5x)/2 * sin(3x-5x)/2=cos 4x
2*cos4x * sin(-x)=cos 4x
2*cos4x * sin(-x) - cos 4x = 0
cos4x * (2*sin(-x) - 1) = 0
два решения
cos4x=0 4 x = Pi/2 + kPi x = Pi/8 + kPi/4
sin(x) = -1/2
x = (-1)^(n+1)Pi/6 + nPi