π/2 = 90° ⇒ π/4 = 45° ⇒ π/8 = 45°/2 = 22°30'
Avem formula:
tg (x/2) = sinx / cosx+1
tg (45°/2) = sin45° / (cos45° + 1)
tg (22°30') = √2/2 / 1+(√2/2)
tg (22°30') = √2/2 / (2+√2)/2
tg (22°30') = √2/2 × 2/(2+√2)
tg (22°30') = √2 / (2+√2)
tg (22°30') = √2 / √2(√2+1)
tg (22°30') = 1 / √2+1
tg (22°30') = √2-1 / 2-1
tg (22°30') = √2-1
