Question

Using the formula, tan2theta = 2tan theta/1-tan^2theta

Obtain the value of tan15°

Answer 1

Answer:

2 - √3

Step-by-step explanation:

let theta =∝

tan 2 theta = 2 tan theta/1-tan^2 theta

tan2∝ = 2tan ∝/1-tan^2∝

tan30 = 2 tan 15/1-tan^215

2k ÷ 1 - k² = 1/√3

2√3k = 1 - k²

k² + 2√3k- 1 = 0

k = {- 2√3 ± √ (12 +4  )}/2

k = { ± 4 - 2√3 } /2

k = ± 2 - √3

k =  2 - √3

tan 15 = 2 - √3