sin(π/4+θ)*sin(π/4-θ)=2/5,则cos2θ=
问题描述：
sin(π/4+θ)*sin(π/4-θ)=2/5,则cos2θ=
答
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