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If tanx/tany = a, find the value of sin (x + y)/sin (x - y)?

If tanx/tany = a, find the value of sin (x + y)/sin (x - y)? Correct Answer (a + 1)/(a - 1)

Given:

tanx/tany = a

Formula used:

sin (x + y) = sinx.cosy + cosx.siny

sin (x - y) = sinx.cosy - cosx.siny

tan θ = sin θ/cos θ 

Calculation:

∵ tanx/tany = a

⇒ sinx.cosy/cosx.siny = a

⇒ sinx.cosy = a × (cosx.siny)      ------(1)

∵ sin (x + y)/sin (x - y) = (sinx.cosy + cosx.siny)/(sinx.cosy - cosx.siny)

⇒ /

⇒ /

⇒ (a + 1)/(a - 1)

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