求证sin^4a=1/8(3-4cos^2a+cos4a)

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求证sin^4a=1/8(3-4cos^2a+cos4a)

求证sin^4a=1/8(3-4cos^2a+cos4a)
求证sin^4a=1/8(3-4cos^2a+cos4a)

求证sin^4a=1/8(3-4cos^2a+cos4a)
sin^4a=sin^2a(1-cos^2a)
=sin^2a-sin^2acos^2a
=(1-cos2a)/2-1/4sin^2 2a
=(1-cos2a)/2-1/4*(1-cos4a)/2
=1/8(3-4cos^2a+cos4a)