Cos (x+y) / cos (x) sin (y) = cot (y) - tan (x)

So there is an identity we'll need to use to solve this:

cos (x+y) = cosxcosy - sinxsiny

replace the numerator with the right hand side of that identity and we get:

(cosxcosy - sinxsiny) / cosxsiny

Separate the numerator into 2 fractions and we get:

cosxcosycosxsiny - sinxsiny/cosxsiny

the cosx's cancel on the left fraction, the siny's cancel on the right fraction and we're left with:

cosy/siny - sinx/cosx

which simplifies to:

coty - tanx