Question

Find the value of tan π/8

Answer 1

let Ф = π/8
2Ф = π/4  

    tan 2Ф = 1  = 2 tan Ф / [ 1 - tan² Ф ]

   1  - tan² Ф = 2 tan Ф

   tan² Ф + 2 tan Ф - 1 = 0

   tan Ф  =  1/2 [ -2 +- √(4 +4) ]  = -1 +- √2

   tan π/8 is > 0 So,  tan π/8 = √2 - 1

Answer 2

Answer:

(√2 -1)

Step-by-step explanation:

we know that

Tan A/2 = (1-cosA)/(sinA)

So,

tan 45/2 = (1-cos45)(sin45)

=(√2 -1)/1

therefore tan(π/8) = (√2 -1)