2cos^2x-7cosx=2sin^2x
2cos^2(x)-7cos(x)=2sin^2(x)
2cos^2(x)-7cos(x)-2(1-cos^2(x))=0
4cos^2(x)-7cos(x)-2=0
cos(x)=t
4*t^2-7t-2=0
D=b^2-4ac=81
t1,2=(-b±sqrt(D))/2a
t1=(7-9/8=-1/4
t2=(7+9)/8=2>1 - не удовлетворяет ОДЗ
cos(x)=-1/4
x=±arccos(-1/4)+2*pi*n
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2cos^2(x)-7cos(x)=2sin^2(x)
2cos^2(x)-7cos(x)-2(1-cos^2(x))=0
4cos^2(x)-7cos(x)-2=0
cos(x)=t
4*t^2-7t-2=0
D=b^2-4ac=81
t1,2=(-b±sqrt(D))/2a
t1=(7-9/8=-1/4
t2=(7+9)/8=2>1 - не удовлетворяет ОДЗ
cos(x)=-1/4
x=±arccos(-1/4)+2*pi*n