cos2θ=根号2/3,则sin^4θ+cos^4θ=

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cos2θ=根号2/3,则sin^4θ+cos^4θ=

cos2θ=根号2/3,则sin^4θ+cos^4θ=
cos2θ=根号2/3,则sin^4θ+cos^4θ=

cos2θ=根号2/3,则sin^4θ+cos^4θ=
sin^4a+cos^4a
=(sin²a+cos²a)²-2sin²acos²a
=1-(1/2)sin²2a
=1-(1/2)[1-cos²2a]
=11/18

cos2θ=√2/3
(cos2θ)^2=2/9
(sin2θ)^2=7/9
sin^4θ+cos^4θ
=(sin^2θ+cos^2θ)^2-2sin^2θcos^2θ
=1-2*7/9*2/9
=53/81

sin^4θ+cos^4θ=(sin^2θ+cos^2θ)^2-2sin^2θcos^2θ=1-1/2*(sin2θ)^2
(sin2θ)^2=1-(cos2θ)^2=5/9
sin^4θ+cos^4θ=1-5/18=13/18