If sin⁡xsin⁡y=12,cos⁡xcos⁡y=32,where x,y∈0,π2, then the value of tan (x+y) is equal to

If $\frac{\mathrm{sin}\mathrm{x}}{\mathrm{sin}\mathrm{y}}=\frac{1}{2},\frac{\mathrm{cos}\mathrm{x}}{\mathrm{cos}\mathrm{y}}=\frac{3}{2},$where $\mathrm{x},\mathrm{y}\in \left(0,\frac{\mathrm{\pi }}{2}\right)$, then the value of tan (x+y) is equal to

1. A

$\sqrt{13}$

2. B

$\sqrt{14}$

3. C

$\sqrt{17}$

4. D

$\sqrt{15}$

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