已知tan(a/2-pai/2)=根号3/2 求cos(a+pai/3)的值

不小心来帮你了
→tan(a/2)=-√3/2
→tan2(a/2)=2tan(a/2)/(1-tan(a/2)*tan(a/2))
→tana=-4√3
→sina=4√3/7,cosa=-1/7
→cos(a+π/3)=1/2*cosa+√3/2*sina=11/14