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数学
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已知sinx-cosx=1/2,求sin^4x+cos^4x的值
人气:242 ℃ 时间:2020-03-23 23:29:56
解答
sin^4x+cos^4x=(sin^2x+cos^2x)-2sin^2xcos^2x=1-2sin^2xcos^2x
因为sinx-cosx=1/2
所以(sinx-cosx)^2=1/4
(sinx-cosx)^2==1-2sinxcosx
即 1-2sinxcosx=1/4
sinxcosx=3/8
sin^2xcos^2x=9/64
sin^4x+cos^4x=(sin^2x+cos^2x)-2sin^2xcos^2x=1-2sin^2xcos^2x=1-2*(9/64)
=23/32
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