已知cos(x+∏/4)=1/3,求cos(2x)/cos(x-∏/4)的值（∏是圆周率）

题目

已知cos(x+∏/4)=1/3,求cos(2x)/cos(x-∏/4)的值（∏是圆周率）

答案

因为cos(x+π/4)=1/3
cos(x-π/4)=cos(x+π/4-π/2)=sin(x+π/4)
所以cos(2x)/cos(x-π/4)
=sin(2x+π/2)/sin(x+π/4)
=sin[2(x+π/4)]/sin(x+π/4)
=2sin(x+π/4)cos(x+π/4)/sin(x+π/4)
=2cos(x+π/4)
=2*1/3
=2/3