sin(x+y)/sin(x-y)=(a+b)/(a-b) then tanx/tany=?

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(tan x)/(tan y) = [(sin x)/(cos x)]/[sin y)/(cos y) = [(sin x)(cos y)]/[(cos x)(sin y)]

[sin (x+y)]/[sin (x - y)] = (a + b)/(a - b)

sin (x + y) = a + b

(sin x)(cos y) + (cos x)(sin y) = a + b

(sin x)(cos y) = a

(cos x)(sin y) = b

(tan x)/(tan y) = a/b

If sin(x+y)/sin(x-y)=(a+b)/(a-b) then tanx/tany=?

sin(x+y)/sin(x-y)=(sinxcosy+cosxsiny)/(sinxcosy-cosxsiny) divide both numerator and denominator by

cosxcosy and get (tanx+tany)/(tanx-tany)

Let a=tanx, b=tany and have sin(x+y)/sin(x-y)=(a+b)/(a-b) and also tanx/tany=a/b

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