已知sin^4θ-cos^4θ=5/9,求cos4θ的值.

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已知sin^4θ-cos^4θ=5/9,求cos4θ的值.已知sin^4θ-cos^4θ=5/9,求cos4θ的值.已知sin^4θ-cos^4θ=5/9,求cos4θ的值.sin^4θ-cos^4θ

已知sin^4θ-cos^4θ=5/9,求cos4θ的值.
已知sin^4θ-cos^4θ=5/9,求cos4θ的值.

已知sin^4θ-cos^4θ=5/9,求cos4θ的值.
sin^4θ-cos^4θ=(sin²θ+cos²θ)(sin²θ-cos²θ)=sin²θ-cos²θ=5/9
cos4θ=2cos²(2θ)-1=2*(cos²θ-sin²θ)²-1=2*(-5/9)²-1=50/81-1=-31/81

sin^4a-cos^4a=5/9
(sin²a+cos²a)(sin²a-cos²a)=5/9
cos2a=-5/9
cos4a=2cos²2a-1=-31/81