Find value

Question

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

Answer 1

(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

Answer 2

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