已知sin(π/4 + α)*sin(π/4 - α)=1/6,α属于(1/2*π,π),求sin4α的值
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![已知sin(π/4 + α)*sin(π/4 - α)=1/6,α属于(1/2*π,π),求sin4α的值](/uploads/image/z/8569173-21-3.jpg?t=%E5%B7%B2%E7%9F%A5sin%28%CF%80%2F4+%2B+%CE%B1%29%2Asin%EF%BC%88%CF%80%2F4+-+%CE%B1%EF%BC%89%3D1%2F6%2C%CE%B1%E5%B1%9E%E4%BA%8E%EF%BC%881%2F2%2A%CF%80%2C%CF%80%EF%BC%89%2C%E6%B1%82sin4%CE%B1%E7%9A%84%E5%80%BC)
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已知sin(π/4 + α)*sin(π/4 - α)=1/6,α属于(1/2*π,π),求sin4α的值
已知sin(π/4 + α)*sin(π/4 - α)=1/6,α属于(1/2*π,π),求sin4α的值
已知sin(π/4 + α)*sin(π/4 - α)=1/6,α属于(1/2*π,π),求sin4α的值
根据公式sinα ·sinβ=-0.5 [cos(α+β)-cos(α-β)]
所以sin(π/4+α)sin(π/4-α)=-0.5[cos(π/2) --cos(2α)]===0.5cos(2α)==1/6
所以cos(2α)==1/3
因为α∈(π/2,π),所以2α∈(π,2π).
所以sin2α==-2√2/3
所以sin4α==2sin2α * cos2α ====-4√2/9
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