Question

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

Answer 1

Given trigonometric equation is,

We know the componendo and dividendo property, that is,

So by applying this componendo and dividendo property in the given trigonometric equation,

{sin(x+y) + sin(x-y)} / {sin(x+y) - sin(x-y)} = (a+b+a-b)/a+b-a+b) -------(1)

We know that,

&

Using above formula in the given equation (1),

{2 sin (x+y+x-y)/2 . cos (x+y-x+y)/2} / {2 cos (x+y+x-y)/2 . sin (x+y-x+y)/2} = 2a / 2b

=> 2 sin x . cos y / 2 cos x . sin y = a/b

=> (sin x / cos x)(cos y / sin y) = a/b

=> tan x . cot y = a/b

We know that cot y = 1 / tan y

=> tan x / tan y = a/b

{So the value of tanx/tany is a/b}

{Hope It Helps}