1.已知cos2θ=根号2/3,则sin^4+cos^4的值为________.

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1.已知cos2θ=根号2/3,则sin^4+cos^4的值为________.1.已知cos2θ=根号2/3,则sin^4+cos^4的值为________.1.已知cos2θ=根号2/3,则sin

1.已知cos2θ=根号2/3,则sin^4+cos^4的值为________.
1.已知cos2θ=根号2/3,则sin^4+cos^4的值为________.

1.已知cos2θ=根号2/3,则sin^4+cos^4的值为________.
因为(sinθ^2+cos^θ2)^2=1
用完全平方
sinθ^4+cosθ^4=1-2sinθ^2cosθ^2
再用倍角公式
2sin^2cos^2=0.5(2sinθcosθ)^2
cos2θ=2/3
(sin2θ)^2=5/9
1-0.5(5/9)=13/18

sin^4+cos^4是sinθ^4+cosθ^4吗?

cos2θ=2cosθ方-1
2cosθ方-1=根号2/3所以cosθ可求那么sinθ也能求
sin^4+cos^4变形为(sin方+cos方)乘以(sin方-cos方)就变成了1乘以(sin方-cos方)
sin方-cos方可以写成(sin+cos)乘以(sin-cos)
上面已经得出了sin与cos的值带入即可得sin^4+cos^4的值