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pinkdream
@pinkdream
July 2022
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4sin^2 x/2+8cosx/2-7=0
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Volosatya1kolenka
4 sin^2 (x/2) + 8 cos (x/2) -7 = 0Пусть x/2=yТогда:4sin^2(y) + 8cos(y) -7=04(1-cos^2(y)) + 8cos(y)-7=04-4cos^2(y)+8cos(y)-7=04cos^2(y)-8cos(y)+3=0D=64-48=16cos(y)=8+4/8 = 12/8 - не существуетcos(y)=8-4/8 = 4/8 = 1/2 ->y=pi/3+2pi*n и y=pi-pi/3+2pi*m = 2pi/3+2pi*m y1=pi/3+2pi*n , тогда x=2pi/3+4pi*ny2=2pi/3+2pi*m , тогда x=4pi/3+4pi*mОтвет: x=2pi/3+4pi*n , x=4pi/3+4pi*m
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