若sinα=1/2,则sin(π/4-α)cos(π/4-α)=
问题描述：
若sinα=1/2,则sin(π/4-α)cos(π/4-α)=
答
sin(π/4-a)cos(π/4-a)
=1/2*2sin(π/4-a)cos(π/4-a)
=1/2*sin[2(π/4-a)]
=1/2*sin(π/2-2a)
=1/2*cos(2a)
=1/2*[1-2(sina)^2]
=1/2*[1-2*(1/2)^2]
=1/4 .