sin(45°+α)sin(45°-α)=1/6,α∈(90°,180°),求sin4α

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sin(45°+α)sin(45°-α)=1/6,α∈(90°,180°),求sin4α
sin(45°+α)sin(45°-α)=1/6,α∈(90°,180°),求sin4α

sin(45°+α)sin(45°-α)=1/6,α∈(90°,180°),求sin4α
sin(45°+α)sin(45°-α)=1/6
∵sin(45°-α)=sin[90º-(45º+α)]=cos(45º+α)
∴sin(45°+α)cos(45°+α)=1/6
两边同时乘以2
2sin(45°+α)cos(45°+α)=1/3
根据二倍角正弦公式：
2sin(45°+α)cos(45°+α)=sin[2(45º+α)]==1/3
∴sin(90º+2α)=1/3
即 cos2α=1/3
∴cos4α=2(cos2α)^2-1=2/9-1=-7/9

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