已知sin(π/4 +α)*sin(π/4 -α)=1⼀6,α∈(π/2,π),求sin4α

2025-03-12 21:40:08
推荐回答(1个)
回答1:

sin(π/4 -α)=cos[π/2-(π/4 -α)]=cos(π/4 +α)
sin2(π/4 +α)=2sin(π/4 +α)*sin(π/4 -α)=1/3=cos2α
α∈(π/2,π),2α∈(π,2π)所以sin2α<0
sin2α=-(2根号2)/3
sin4α=-(4根号2)/9