Question

求tan(π/8)

Answer 1

let x = π/8

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

or tanπ/8 = -1+√2 ( rejected)

tanπ/8 = -1 +√2