sin(π/4+α)sin（π/4-α）=1/6,α∈（0.π/2）,求：sin4α的值

题目

sin(π/4+α)sin（π/4-α）=1/6,α∈（0.π/2）,求：sin4α的值

答案

sin(π/4+α)sin(π/4-α)
=-0.5[cos(π/2) --cos(2α)]
=0.5cos(2α)
=1/6
cos(2α)=1/3
sin(2α)=2根号2/3
sin4α=2sin2α*cos2α
=4根号2/9