Question

已知sin(π/4-x)=12/13,0<x<3π/4,求cos2x/cos(π/4+x)

Answer 1

解析：
由已知得：sin(π/4-x)=sin(π/2 - π/4 -x)=cos( π/4 +x)=12/13
因为0<x<3π/4，那么： π/4 < π/4 +x<π
所以可得：sin( π/4 +x)=√[1- cos²( π/4 +x)]=5/13
那么：
cos2x/cos(π/4+x)
=sin(π/2 + 2x)/cos(π/4+x)
=2sin(π/4+x)cos(π/4+x)/cos(π/4+x)
=2sin(π/4+x)
=10/13