Let $a$ and $b$ be angles such that $\sin (a + b) = \frac{3}{4}$ and $\sin (a - b) = \frac{1}{2}.$  Find $\frac{\tan a}{\tan b}.$
Question:
Let $a$ and $b$ be angles such that $\sin (a + b) = \frac{3}{4}$ and $\sin (a - b) = \frac{1}{2}.$  Find $\frac{\tan a}{\tan b}.$
Answer:
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Let $a$ and $b$ be angles such that $\sin (a + b) = \frac{3}{4}$ and $\sin (a - b) = \frac{1}{2}.$  Find $\frac{\tan a}{\tan b}.$
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