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JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

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Application +4 | -1
If sin    (x+y)sin⁡    (x−y)=a+ba−b\frac{{\mathrm{sin}\,\,\mathrm{\;}\left( {x + y} \right)}}{{\sin \,\,\;\left( {x - y} \right)}} = \frac{{a + b}}{{a - b}}, then tan⁡  xtan⁡  y\frac{{\tan \,\,x}}{{\tan \,\,y}} is equal to
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Correct option: B
ab\frac{a}{b}
Option B (ab\frac{a}{b}) is correct because by applying the componendo and dividendo rule and trigonometric identities, the ratio of tangents simplifies to ab\frac{a}{b}.

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