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tinabashkatova
@tinabashkatova
July 2022
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Формулы приведения, формулы сложения и двойного угла. Упростить:
1) cos(2П-3x)cos x+sin 3x cos(3П/2 + x)
2) sin(П-3x)cos x + cos3x cos(3П/2-ч)
3) sin a sin 2a + cos(П/2+a)
4) 3cos^2 x + 3sin^2 x-6
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Answers & Comments
Maria1622
1)cos3x*cosx+sin3x*sinx=cos(3x-x)=cos2x
2)sin3x*cosx-cos3x*sinx=sin(3x-x)=sin2x
3)sina*sin2a-sina=sina*2*sina*cosa-sina=2sin^2a*cosa-sina=sina*(2sina-1)
sina*(2sina-1)=0
sina=0 2sina=1
a=Пn,n€Z sina=½
a=(-1)^n* П/6+Пn,n€Z
4)3cos^2x+3sin^2x-6=3(cos^2x+sin^2x-2)=3(1-2)=3*(-1)=-3
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Answers & Comments
2)sin3x*cosx-cos3x*sinx=sin(3x-x)=sin2x
3)sina*sin2a-sina=sina*2*sina*cosa-sina=2sin^2a*cosa-sina=sina*(2sina-1)
sina*(2sina-1)=0
sina=0 2sina=1
a=Пn,n€Z sina=½
a=(-1)^n* П/6+Пn,n€Z
4)3cos^2x+3sin^2x-6=3(cos^2x+sin^2x-2)=3(1-2)=3*(-1)=-3