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If tanx/tany = a, find the value of sin (x + y)/sin (x - y)?1. a2 -12. (a + 1)/(a - 1)3. (a - 1)/(a + 1)4. 2a |
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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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