Fewpal
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Find the value of tan π/8

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Solution:

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 

Therefore,  tan π/8 = √2 - 1

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