x∈(π,3π/2),sin^4X+cos^4X=5/9,求sin^2X拜托各位了 3Q

x∈(π,3π/2),sin^4X+cos^4X=5/9,求sin^2X拜托各位了 3Q
x∈(π,3π/2),sin^4X+cos^4X=5/9,求sin^2X拜托各位了 3Q

x∈(π,3π/2),sin^4X+cos^4X=5/9,求sin^2X拜托各位了 3Q
由已知sin 4 X+ cos 4 X = 5/9 => (sin 2 X + cos 2 X) 2 –2sin 2 Xcos 2 X = 5/9 => 1 – 2sin 2 Xcos 2 X= 5/9 => 2sin 2 Xcos 2 X = 4/9 => sin 2 Xcos 2 X= 2/9 => sin 2 X(1 – sin 2 X) = 2/9 => 9sin 2 X(1– sin 2 X) = 2 => 9sin 4 X– 9sin 2 X + 2 = 0=> (3sin 2 X– 2)(3sin 2 X– 1) = 0 => (3sin 2 X– 2) = 0或者(3sin 2 X– 1) = 0 => sin 2 X = 2/3 或者 1/3 .