Question

高一数学题、求教

化简:2sin(π/4+α)sin(π/4-α)

Answer 1

2sin(π/茄隐4+α)sin(π/清纳罩4-α)
=2sin(π/答闹4+α)cos(π/4+α)
=sin(π/2+2α)
=cos2α

Answer 2

2sin(π/茄隐4+α)sin(π/清纳罩4-α)
=2sin(π/答闹4+α)cos(π/4+α)
=sin(π/2+2α)
=cos2α

Answer 3

2sin(π/4+α)sin(π/4-α)
=2sin(π/4+α)cos(π/4+α)
=sin(π/毁纯2+2α)
=cos2α
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Answer 4

积化和差公式旦宴为 sinαsinβ=[cos(α-β)-cos(α+β)]/2
所或销以2sin(π/4+α)sin(π/衫迟游4-α)=cos(π/4+α-π/4+α)-cos(π/4+α+π/4-α)=cos2α-cosπ/2=cos2α