tan θ 2 ͷஔΛ͢Δɻ tan θ = sin(θ 2 + θ 2 ) cos(θ 2 + θ 2 ) = 2 sin θ 2 cos θ 2 cos2 θ 2 − sin2 θ 2 = 2 tan θ 2 1 − tan2 θ 2 ʢͱࢠΛ cos2 θ 2 Ͱׂͬͨʣ = 2t 1 − t2 ͜͜Ͱɼਤܗͱͯ͠ͷ tan θ ͷఆٛʹΑͬͯɼҰͭͷ͕֯ θɼఈล 1 − t2ɼߴ͞ 2t ͷ֯ࡾ֯ܗΛඳ͘ɻࡾฏํͷఆཧΑΓࣼล θ 1 − t2 2t l l = √ (1 − t2)2 + (2t)2 = √ (1 + 2t2 + t4) = (1 + t2) ਤΑΓɼ cos θ = 1 − t2 1 + t2 sin θ = 2t 1 + t2 sin θ ͷ྆ลΛ θ Ͱඍͯ͠ɼ cos θ = dt dθ · d dt ( 2t 1 + t2 ) = dt dθ · 2 · (1 + t2) − 2t · 2t (1 + t2)2 1 − t2 1 + t2 = dt dθ · 2(1 − t2) (1 + t2)2 dθ = 2dt 1 + t2 ·ͨɼcos θ ͷࣜʹண͠ɼ (1 + t2) cos θ = 1 − t2 (1 + cos θ)t2 = 1 − cos θ t = √ 1 − cos θ 1 + cos θ