If sin (α + β) / sin (α - β) = A / B, then Tan α / Tan β = () Please give me the solution

If sin (α + β) / sin (α - β) = A / B, then Tan α / Tan β = () Please give me the solution

Sin (α + β) / sin (α - β) = A / b (sinacosb + cosasinb) / (sinacosb cosasinb) = A / b. by dividing the numerator on the left by cosacosb, we get: (Tana + tanb) / (Tana tanb) = A / BA (Tana tanb) = b (Tana + tanb) (a-b) Tana = (a + b) tanbtana / tanb = (a + b) / (a-b)

It is proved that sin (a + b) = sinacosb + cosasinb

Proof: as shown in the figure, if ∠ AOC = α, ∠ cod = β, then ∠ AOD = α + β, Ao = 1, ab ⊥ ox intersects ox with B, AC ⊥ OC intersects OC with C, CE ⊥ AB intersects AB with E, CD ⊥ ox intersects ox with D, it is easy to prove △ oBf ∽ ACF ∪ cod = ∠ CAF = β Sin & nbsp; (α + β) = sin ⊥ AOD = AB / AO = AB = AE + EB = AE +