已知sinθ/2+cosθ/2=2√3/3,求sinθ,cos2θ
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已知sinθ/2+cosθ/2=2√3/3,求sinθ,cos2θ
![已知sinθ/2+cosθ/2=2√3/3,求sinθ,cos2θ](/uploads/image/z/8858025-9-5.jpg?t=%E5%B7%B2%E7%9F%A5sin%CE%B8%2F2%2Bcos%CE%B8%2F2%3D2%E2%88%9A3%2F3%2C%E6%B1%82sin%CE%B8%2Ccos2%CE%B8)
sinθ/2+cosθ/2=2√3/3
两边平方
sin²θ/2+cos²θ/2+2sinθ/2cosθ/2=4/3
1+sinθ=4/3
sinθ=1/3
cos2θ
=1-2sin²θ
=7/9
两边平方
sin²θ/2+cos²θ/2+2sinθ/2cosθ/2=4/3
1+sinθ=4/3
sinθ=1/3
cos2θ
=1-2sin²θ
=7/9
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