（全题）已知sin(α+3pi/4)=5/13,cos(pi/4-β)=3/5,且-4/pi小于α小于pi/4,pi/4小于β小于3pi/4,求cos2（α-β）?

题目

（全题）已知sin(α+3pi/4)=5/13,cos(pi/4-β)=3/5,且-4/pi小于α小于pi/4,pi/4小于β小于3pi/4,求cos2（α-β）?

答案

∵sin(α+3π/4)=cos(α+π/4)=5/13
cos(π/4-β)=sin(β+π/4)=3/5
又 -π/4