A) \[\frac{4}{{{a}^{2}}+{{b}^{2}}}\]
B) \[\frac{b}{a}\]
C) \[\frac{a}{b}\]
D) \[\frac{4}{{{a}^{2}}-{{b}^{2}}}\]
Correct Answer: C
Solution :
\[\sin x+\sin y=a\] \[\Rightarrow \] \[2\sin \frac{x+y}{2}\cdot \cos \frac{x-y}{2}=a\] \[\cos x+\cos y=b\] i.e. \[2\cos \frac{x+y}{2}\cdot \cos \frac{(x-y)}{2}=b\] Taking ratio, we have \[\therefore \]\[\frac{2\sin \frac{x+y}{2}\cdot \cos \frac{x-y}{2}}{2\cos \frac{x+y}{2}\cdot \cos \frac{(x-y)}{2}}=\frac{a}{b}\]\[\Rightarrow \]\[\tan \frac{x+y}{2}=\frac{a}{b}\]
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