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

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

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

cos(2x)/cos(x-∏/4)=[(cosx-sinx)(cosx+sinx)]/[2分之根号2倍的(cosx+sinx)]=根号2倍的(cosx-sinx)=2cos(x+∏/4)=2/3