(sin(x+y))/cos(x-y)) = cotxcoty/1+cotxcoty

I'm not sure how to verify this

Start by expanding the part on the left.

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

cos(x-y) = cos(x)cos(y) + sin(x)sin(y)

Then, divide the numerator and denominator bysin(y) because there is cot over on the right.

Do the same with sin(x).

After doing this... I think you forgot to add a plus sign to your identity... :rolleyes:

Which is in fact:

\frac{sin(x+y)}{cos(x-y)} = \frac{cot(x) + cot(y)}{1 + cot(x)cot(y)}