Question

tan8分之派等于多少?怎么化呀

Answer 1

设x = π/8,

则2x = π/4,

tan2x = 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 或 tanπ/8 = -1+√2 ( 舍去)

∴tanπ/8 = -1 +√2