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If tanx/tany = a, find the value of sin (x + y)/sin (x - y)?
1. a2 -1
2. (a + 1)/(a - 1)
3. (a - 1)/(a + 1)
4. 2a

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Best answer
Correct Answer - Option 2 : (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 × (cosx.siny) + cosx.siny]/[a × (cosx.siny) - cosx.siny]

⇒ [cosx.siny(a + 1)]/[cos.siny(a - 1)]

⇒ (a + 1)/(a - 1)

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