sin(π/4+θ)*sin(π/4-θ)=2/5,则cos2θ=

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sin(π/4+θ)*sin(π/4-θ)=2/5,则cos2θ=

sin(π/4+θ)*sin(π/4-θ)=2/5,则cos2θ=
sin(π/4+θ)*sin(π/4-θ)=2/5,则cos2θ=

sin(π/4+θ)*sin(π/4-θ)=2/5,则cos2θ=
因为
π/4-θ=π/2-(π/4+θ)
所以sin(π/4-θ)=sin[π/2-(π/4+θ)]=cos(π/4+θ)
所以
sin(π/4+θ)*sin(π/4-θ)
=sin(π/4+θ)*cos(π/4+θ)
=1/2sin(π+2θ)
=-1/2sin2θ=2/5
所以sin2θ=-4/5
cos2θ=3/5或者-3/5

sin(π/4-θ)=cos[π/2-(π/4-θ)]=cos(π/4+θ)
所以已知条件就变为:sin(π/4+θ)cos(π/4+θ)=2/5
那么2sin(π/4+θ)cos(π/4+θ)=4/5
即sin[2(π/4+θ)]=4/5,即sin(π/2+2θ)=4/5
所以cos2θ=sin(π/2+2θ)=4/5