Question

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Answer 1

Răspuns:

2 - √3

Explicație pas cu pas:

tg 15° = tg (45° - 30°) = (tg 45° - tg 30°) / (1 + tg 45° · tg 30°)

tg 45° = 1 ; tg 30° = √3/3 =>

tg 15° = (³⁾1 - √3/3) /(³⁾1 + 1·√3/3) = [(3-√3)/3] : [(3+√3)/3] =

= [(3-√3)/3] · [3/(3+√3)] = (3-√3)/(3+√3) = (3-√3)·(3-√3)/[(3+√3)(3-√3)] =

= (9-6√3+3) / (9-3) = (12-6√3)/6 = 2 - √3 ≈ 0,268