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bridgelin2
@bridgelin2
July 2022
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Решите, пожалуйста, уравнение. Требуется полный ход решения.
sin(3x-3)=cos(x-1)
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Verified answer
sin(3x-3)=cos(x-1)
sin(3x-3)=sin(pi/2-x+1)
sin(3x-3)-sin(pi/2-x+1)=0
2*sin((3x-3)/2-(pi/2-x+1)/2)*cos((3x-3)/2+(pi/2-x+1)/2)=0
2*sin(3x/2-3/2-pi/4+x/2-1/2)*cos(3x/2-3/2+pi/4-x/2+1/2)=0
sin(2x-2-pi/4)*cos(x-1+pi/4)=0
sin(2x-2-pi/4)=0 или cos(x-1+pi/4)=0
2x-2-pi/4 = pi*k или x-1+pi/4 = pi/2+pi*n
x=1+pi/8 + pi/2*k или x=1-pi/4 + pi/2+pi*n
x=1+pi/8 + pi/2*k или x=1+pi/4+pi*n
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Answers & Comments
Verified answer
sin(3x-3)=cos(x-1)sin(3x-3)=sin(pi/2-x+1)
sin(3x-3)-sin(pi/2-x+1)=0
2*sin((3x-3)/2-(pi/2-x+1)/2)*cos((3x-3)/2+(pi/2-x+1)/2)=0
2*sin(3x/2-3/2-pi/4+x/2-1/2)*cos(3x/2-3/2+pi/4-x/2+1/2)=0
sin(2x-2-pi/4)*cos(x-1+pi/4)=0
sin(2x-2-pi/4)=0 или cos(x-1+pi/4)=0
2x-2-pi/4 = pi*k или x-1+pi/4 = pi/2+pi*n
x=1+pi/8 + pi/2*k или x=1-pi/4 + pi/2+pi*n
x=1+pi/8 + pi/2*k или x=1+pi/4+pi*n