sin(π/4+α)sin(π/4-α)=1/6 求sin2α

题目

sin(π/4+α)sin(π/4-α)=1/6 求sin2α

答案

诱导公式
sin(π/4+α)sin(π/4-α)=1/6
sin(π/4+α)cos(π/4+α)=1/6
2sin(π/4+α)cos(π/4+α)=1/3
sin[2(π/4+α)]=1/3
cos2α=1/3
由(cos2α)^2+(sin2α)^2=1
sin2α=±2√2/9