设函数y=x^2-4px-2的图象经过M(tana,1)N(tanb,1)两点,求tan(a+b)的值

根据韦达定理可得到：
tana+tanb=4p;
tana*tanb=-2;
tan(a+b)=(tana+tanb)/(1-tana*tanb)
=4p/(1+2)=4p/3.
sin2(a+b)=2tan(a+b)/[1+tan^2(a+b)]
=2*(4p/3)/[1+(4p/3)^2]
=24p/(9+16p^2).