cos^2(a+b)+2sin(a+b)cos(a+b)-3sin^2(a+b)
【分母看做1,1=cos^2(a+b)+sin^2(a+b)】
=[cos^2(a+b)+2sin(a+b)cos(a+b)-3sin^2(a+b)]/[cos^2(a+b)+sin^2(a+b)]
【分子分母同時(shí)除以cos^2(a+b)】
=[1+2tan(a+b)-3tan^2(a+b)]/[1+tan^2(a+b)]
又tana,tanb是方程x^2-4x-2=0的兩個(gè)實(shí)根
所以tana+tanb=4,tana*tanb=-2
tan(a+b)=(tana+tanb)/(1-tana*tanb)=4/3
tan^2(a+b)=16/9
所以原式=[1+2tan(a+b)-3tan^2(a+b)]/[1+tan^2(a+b)]
=[1+2*(4/3)-3*(16/9)]/(1+16/9)
=(-5/3)/(25/9)
=-3/5