(sin x*sin 3x)sin^2 x+(cos x*cos 3x)cos^2 x 如何变到1/2[(cos 2x-cos4x)sin^2x+(cos2x+cos4x)cos^2x]

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(sinx*sin3x)sin^2x+(cosx*cos3x)cos^2x如何变到1/2[(cos2x-cos4x)sin^2x+(cos2x+cos4x)cos^2x](sinx*sin3x)sin

(sin x*sin 3x)sin^2 x+(cos x*cos 3x)cos^2 x 如何变到1/2[(cos 2x-cos4x)sin^2x+(cos2x+cos4x)cos^2x]
(sin x*sin 3x)sin^2 x+(cos x*cos 3x)cos^2 x 如何变到1/2[(cos 2x-cos4x)sin^2x+(cos2x+cos4x)cos^2x]

(sin x*sin 3x)sin^2 x+(cos x*cos 3x)cos^2 x 如何变到1/2[(cos 2x-cos4x)sin^2x+(cos2x+cos4x)cos^2x]
sinx*sin3x=(1/2)[cos(x-3x)-cos(x+3x)]=(1/2)[cos2x-cos4x]
cosx*cos3x=(1/2)[cos(x-3x)+cos(x+3x)]=(1/2)[cos2x+cos4x]

用积化和差公式:sinasinb=(1/2)[cos(a-b)-cos(a+b)]
cosacosb=(1/2)[cos(a-b)+cos(a+b)]