sinα-cosα=√2/2,则sin^4α+cos^4α=

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sinα-cosα=√2/2,则sin^4α+cos^4α=
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sinα-cosα=√2/2,则sin^4α+cos^4α=
sinα-cosα=√2/2,则sin^4α+cos^4α=

sinα-cosα=√2/2,则sin^4α+cos^4α=
(sina-cosa)^2=sin^2a-2sinacosa+cos^2a=1-2sinacosa=1/2
sinacosa=1/4
(sin^2a+cos^2a)^2=sin^4a+2sin^2acos^2a+cos^4a=sin^4a+cos^4a+2(sinacosa)^2=1
sin^4a+cos^4a=1-2(sinacosa)^2=1-2*(1/4)^2=7/8
sin^4a+cos^4a=7/8