已知cos2θ=根号2/3,则 sin^4θ+cos^4θ的值为________.已经求到（sin^2θ+cos^2θ）^2=1（sin^2θ+cos^2θ）^2-2sin^2θcos^2θ=1-2sin^2θcos^2θ
问题描述：
已知cos2θ=根号2/3,则 sin^4θ+cos^4θ的值为________.
已经求到（sin^2θ+cos^2θ）^2=1
（sin^2θ+cos^2θ）^2-2sin^2θcos^2θ=1-2sin^2θcos^2θ
答
2sin^2θcos^2θ=2sinθcosθ2sinθcosθ*1/2=1/2sin^2(2θ)
答
sin^4a＋cos^4a
=(sin²a＋cos²a)²－2sin²acos²a
=1－(1/2)sin²2a
=1－(1/2)[1－cos²2a]
=1－(1/2)[1－(2/9)]
=11/18