a-maths

設 θ = A + B 和 α = C + D
如此:
tan θ = tan (A + B)
= (tan A + tan B)/(1 - tan A tan B)
= (1/5 + 1/3)/[1 - (1/5)(1/3)]
= 4/7
tan α = tan (C + D)
= (tan C + tan D)/(1 - tan C tan D)
= (1/8 + 1/7)/[1 - (1/8)(1/7)]
= 3/11
tan (θ + α) = (tan θ + tan α)/(1 - tan θ tan α)
= (4/7 + 3/11)/[1 - (4/7)(3/11)]
= (65/77)/(65/77)
= 1
θ + α = π/4
A + B + C + D = π/4