Question

tana、tanb是方程3x的平方+5x-7=0的两根、求sin（a+b）/cos（a-b）和求cos（a+b）的平方的

Answer 1

tana+tanb=-5/3

tana*tanb=-7/3

sin(a+b)/cos(a-b)=(sinacosb+sinbcosa)/(cosacosb+sinasinb)=(tana+tanb)/(1+tanatanb)=-5/3/(1-7/3)=5/4

tan(a+b)=(-5/3)/(1+7/3)=-1/2

cos^2(a+b)=1/[1+tan^2(a+b)]=5/4