Question

已知sin^4θ-cos^4θ=5/9,求cos4θ的值。

Answer 1

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

Answer 2

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