Question

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Answer 1

You can use the sum of angles identities, then rearrange to put the result in the form of tangents.

`\displaystyle(sin((x+y)))/(sin((x-y)))=(sin((x))cos((y))+cos((x))sin((y)))/(sin((x))cos((y))-cos((x))sin((y)))\\\\=(\left((sin((x))cos((y))+cos((x))sin((y)))/(cos((x))cos((y)))\right))/(\left((sin((x))cos((y))-cos((x))sin((y)))/(cos((x))cos((y)))\right))\\\\=(tan((x))+tan((y)))/(tan((x))-tan((y)))`