sin(a+b)=4/5,tanb=4/3,0

sin(a+b)=4/5,tanb=4/3,0
sin(a+b)=4/5,tanb=4/3,0

sin(a+b)=4/5,tanb=4/3,0
因为00,y=tanx在0到π/2上大于0,在π/2到π上小于0,所以0 tanb=4/3,tanb=(2tanb/2)/[1-(tanb/2)^2]
记tanb/2=x则2x/(1-x^2)=4/3,x=1/2或x=-2(舍）
sinb=(2tanb/2)/[1+(tanb/2)^2]=(2x)/1+x^2=4/5
cosb=[1-(tanb/2)^2]/[1+(tanb/2)^2]=(1-x^2)/(1+x^2)=3/5
sin(a+b)=sinacosb+cosasinb=4/5,该等式可化为
（3/5）sina+(4/5)cosa=4/5,即
3sina+4cosa=4
设tana/2=t则上式可化为6t/(1+t^2)+4(1-t^2)/(1+t^2)=4,解得t=3/4或t=0（舍）
tana=2t/(1-t^2)=24/7