Question

已知sin^4θ +cos^4θ=5/9，求sin2θ 的值

Answer 1

Sin4次方θ+cos4次方θ=5/9
Sin4次方θ+cos4次方θ+2Sin2次方θcos2次方θ-2Sin2次方θcos2次方θ=5/9
(Sin2次方θ+cos2次方θ)2次方-2Sin2次方θcos2次方θ=5/9
1-2Sin2次方θcos2次方θ=5/9
2Sin2次方θcos2次方θ=4/9
4Sin2次方θcos2次方θ=8/9
(2Sinθcosθ)2次方=8/9
(sin2θ)2次方=8/9
sin2θ=±2√2/3

Answer 2

sin^4x+cos^4x
=(sin^2x+cos^2x)^2-2sin^2xcos^2x
=1-2sin^2xcos^2x=5/9
2sin^2xcos^2x=4/9
4sin^2xcos^2x=8/9
(2sinxcosx)^2=8/9
sin2x=+-(8/9)^(1/2)
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