已知tan(π/4 - x)=-1/2 ,则cos(2x)=

tan(π/4 - x)*(1+tan(π/4)*tan(x))=tan(π/4)-tan(x)
易当做方程解出tan(x)=3=t
万能公式
cos(2x)=(1-t^2)/(1+t^2)=-0.8

tan(π/4 - x)=(tanπ/4+tanx)/(1-tanπ/4tanx)
=(1+tanx)/(1-tanx)=-1/2 得到tanx=-3
cos(2x)=sin^2(x)-cos^2(x)
=(sin^2(x)-cos^2(x))/(sin^2(x)+cos^2(x))
=(1-tan^2(x))/(1+tan^2(x))
带tanx=-3入式子得到
原式=（1-（-3）^2)/(1+(-3)^2)
=-8/10