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
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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