Question

已知sin＾4θ +cos^4θ=5/9,求sin2θ 的值

Answer 1

sin＾4θ +cos^4θ=5/9,

(sin＾2θ +cos^2θ)^2-2 sin＾2θ cos^2θ=5/9,

1-2 sin＾2θ cos^2θ=5/9,

2 sin＾2θ cos^2θ=4/9,

4 sin＾2θ cos^2θ=8/9,

即(2sinθcosθ) ^2=8/9,

(sin2θ)^2=8/9,

sin2θ=±2√2/3.