If `(sinx)/(siny)=1/2,(cosx)/(cosy)=3/2` , where `x , y , in (0,pi/2),` then the value of `"tan"(x+y)` is equal to (a)`sqrt(13)` (b) `sqrt(14)` (c) `sqrt(17)` (d) `sqrt(15)`

Explanation

To solve the problem, we need to find the value of \( \tan(x+y) \) given the equations:

\[ \frac{\sin x}{\sin y} = \frac{1}{2} \quad \text{and} \quad \frac{\cos x}{\cos y} = \frac{3}{2} \]

### Step 1: Express \( \tan x \) and \( \tan y \)

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