已知α∈(0,π/4) sin(π/4-α)=7/25 则cos2α

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已知α∈(0,π/4)sin(π/4-α)=7/25则cos2α已知α∈(0,π/4)sin(π/4-α)=7/25则cos2α已知α∈(0,π/4)sin(π/4-α)=7/25则cos2αα∈(0

已知α∈(0,π/4) sin(π/4-α)=7/25 则cos2α
已知α∈(0,π/4) sin(π/4-α)=7/25 则cos2α

已知α∈(0,π/4) sin(π/4-α)=7/25 则cos2α
α∈(0,π/4)
0<π/4-α<π/4
cos(π/4 -α)>0
cos(π/4 -α)=√[1-sin²(π/4-α)]=√[1-(7/25)²]=24/25
cos(2α)
=sin(π/2 -2α)
=sin[2(π/4-α)]
=2sin(π/4-α)cos(π/4-α)
=2×(7/25)×(24/25)
=336/625