Math, asked by PriyanshuPrasad, 1 year ago

find the value of tan π/8

Answers

Answered by MarkAsBrainliest
7
Answer :

We know that,

π/4 = 2 × π/8

Now, taking (tan) to both sides, we get

tan(π/4) = tan(2 × π/8)

⇒ 1 = {2 tan(π/8)}/{1 - tan²(π/8)},

since tan2A = (2 tanA)/(1 - tan²A)

⇒ 1 - tan²(π/8) = 2 tan(π/8)

⇒ 1 - x² = 2x, let x = tan(π/8)

⇒ x² + 2x - 1 = 0

So, x = [- 2 ± √{2² - 4 × 1 × (-1)}]/(2 × 1)

= (- 2 ± 2√2)/2

= - 1 ± √2

Since, x = tan(π/8)

Here, - 1 - √2 = - tan(π/8)

but (- 1 + √2) = tan(π/8)

Therefore, tan(π/8) = √2 - 1

#MarkAsBrainliest

PriyanshuPrasad: can u answer my previous question
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