find the value of tan π/8
Answers
Answered by
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
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
Similar questions