Question

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

Answer 1

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