已知tana/2=-1/2,求cos（a-π/6）的值
问题描述：
已知tana/2=-1/2,求cos（a-π/6）的值
答
（3根3+4）/10
答
根据万能公式
sina=(2tana/2)/(1+tan²a/2)
=[2×(-1/2)]/[1+(-1/2)²]
=-1/(5/4)
=-4/5
cosa=(1-tan²a/2)/(1+tan²a/2)
=[1-(-1/2)²]/[1+(-1/2)²]
=(3/4)/(5/4)
=3/5
cos(a-π/6)=cosacosπ/6+sinasinπ/6
=3/5×(√3)/2-4/5×1/2
=(3√3-4)/10