已知函数f(x)=sinx+sin[x+(π/2),x∈R,若f(α)=3/4,则sin2α=?

f(x)=sinx+sin[x+(π/2)
=sinx+cosx
f(α)=sinα+cosα=3/4
因为 sin2α=2sinαcosα
所以sin2α=2sinαcosα=(sinα+cosα)^2-[(sinα)^2+(cosα)^2]
=(3/4)^2-1
=9/16-1
=-7/16