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If sin A+sin B=alpha\ a n d\ cos A+cos B...

If `sin A+sin B=alpha\ a n d\ cos A+cos B=beta,` then write the value of `tan((A+B)/2)dot`

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`frac{alpha}{beta}=frac{2 sin (frac{A+B}{2}) cdot cos (frac{A-B}{2})}{2 cos (frac{A+B}{2}) cdot cos (frac{A-B}{2})}`

`frac{alpha}{beta}=tan (frac{A+B}{2})`

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