Find the value of tan π/8
Answers
Answered by
286
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
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
Answered by
1
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)
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