tana=√3
tang(a/2)=√3/3
∵cos2a= -1/2
∴cos^2 a-sin^2 a= -1/2
(cos^2 a-sin^2 a) / (cos^2 a+sin^2 a)= -1/2
(1-tan^2 a) / (1+tan^2 a)= -1/2
2-2tan^2 a= -1-tan^2 a
tan^2 a=3
tana=±√3 (據(jù)a范圍舍去負值)
∵tana=tan[2*(a/2)]
∴√3=[2tan(a/2)] / [1-tan^2 (a/2)]
√3tan^2 (a/2)+2tan(a/2)-√3=0
[√3tan(a/2)-1] * [tan(a/2)-√3]=0
tan(a/2)=√3/3或√3
∵a∈(π/4,π/2)
∴a/2∈(π/8,π/4)
∴tan(a/2)=√3/3^什么意思舉例說吧：3^2就是3的2次方