题目

已知α∈(0,π/4) sin(π/4-α)=7/25 则cos2α

提问时间：2021-04-09

答案

α∈(0,π/4)
0<π/4-α<π/4
cos(π/4 -α)>0
cos(π/4 -α)=√[1-sin²(π/4-α)]=√[1-(7/25)²]=24/25
cos(2α)
=sin(π/2 -2α)
=sin[2(π/4-α)]
=2sin(π/4-α)cos(π/4-α)
=2×(7/25)×(24/25)
=336/625