tan b=sin b/cos b=sin a*cos(a+b)/cos b=sin a*cos a-sin a*sin b/cos b
tan b(1+（sin a）^2)=sin a*cos a
tan b=sin a*cos a/(1+(sin a)^2)
所以tanβ=sinαcosα/（1+sinαsinα)
=(1/2sin2α)/(1+(1+sin2α)/2)
=sin2α/(3-cos2α)
求导=-2（3cos2α-1)/(3-cos2α)^2=0
得cos2α=1/3
所以sin α=根号3/3 cos α=根号6/3
得tan β=根号2/4
tan α =1/根号2
得tan(α+β)=根号2