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If (sin(x+y))/(sin(x-y)) = (a+b)/(a-b), then the value of (tan x)/(tan y) is

1. (b)/(a)
2. (a)/(b)
3. ab
4. None of these

Correct answer: (a)/(b)

Solution

By componendo and dividendo, [sin(x+y)+sin(x-y)]/[sin(x+y)-sin(x-y)] = (a+b+a-b)/(a+b-a+b) = a/b. The left side is (2 sinx cosy)/(2 cosx siny) = tanx/tany, so tanx/tany = a/b.

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