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

题目

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

答案

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=...