已知sina+cosa=m 求sina*cosa 和 sin^4a+cos^4a的值
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已知sina+cosa=m 求sina*cosa 和 sin^4a+cos^4a的值
sina+cosa=m
(sina+cosa)^2=m^2
1+2sinacosa=m^2
2sinacosa=m^2-1
sinacosa=(m^2-1)/2
sin^2acos^2a=(m^2-1)^2/4
sin^4a+cos^4a
=(sin^2a+cos^2a)^2-2sin^2acos^2a
=1-2sin^2acos^2a
=1-2*(m^2-1)^2/4
=1-(m^2-1)^2/2
=1-(m^4-2m^2+1)/2
=m^2/2+1/2-m^4/2
(sina+cosa)^2=m^2
1+2sinacosa=m^2
2sinacosa=m^2-1
sinacosa=(m^2-1)/2
sin^2acos^2a=(m^2-1)^2/4
sin^4a+cos^4a
=(sin^2a+cos^2a)^2-2sin^2acos^2a
=1-2sin^2acos^2a
=1-2*(m^2-1)^2/4
=1-(m^2-1)^2/2
=1-(m^4-2m^2+1)/2
=m^2/2+1/2-m^4/2
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