已知0＜a＜π/2,tana/2+1/(tana/2)=5/2,试求sin（a-π/3)的值

已知0＜a＜π/2,tana/2+1/(tana/2)=5/2,试求sin（a-π/3)的值
已知0＜a＜π/2,tana/2+1/(tana/2)=5/2,试求sin（a-π/3)的值

已知0＜a＜π/2,tana/2+1/(tana/2)=5/2,试求sin（a-π/3)的值
tana/2+1/(tana/2)=5/2
解上述方程,得
tana/2=1/2或tana/2=2（舍去）.
已知0＜a＜π/2,
可知,sina/2=1/√5,cosa/2=2/√5.
sina=2sina/2cosa/2=4/5,cosa=(cosa/2)^2-(sina/2)^2=3/5.
sin（a-π/3)=sinacosπ/3-cosasinπ/3=4/5*1/2-3/5*√5/2=(4-3√5)/10.