请问怎么解tan（π/8）的精确值,用倍角公式是精确值,如cos(π/4)=根2/2

Question

请问怎么解tan（π/8） 的精确值,用倍角公式
是精确值,如 cos(π/4 )= 根2/2

Answer 1

tanπ/4 = 2tanx/(1-(tanx)^2)
1 = 2tanπ/8 / (1- (tanπ/8)^2 )
1- (tanπ/8)^2 = 2 tanπ/8
(tanπ/8)^2 + 2tanπ/8 -1 =0
tanπ/8 = -1 +√2
or tanπ/8 = -1-√2 ( 舍)
tanπ/8 = -1 +√2