[tex]*\frac{cos(x+y)}{cos\ x\ sin\ y} =cot\ y-tan\ x\\\\
\frac{cos \ x \ cos \ y \ - \ sen \ x \ sen \ y}{cos \ x \ sin \ y}
\\\\ \frac{cos \ x \ cos \ y}{cos \ x \ sin \ y} - \frac{sen \ x \ sen \ y}{cos \ x \ sin \ y}
\\\\ Simplify
\\\\
\frac{cos \ y}{sin \ y} - \frac{sen \ x}{cos \ x}
\\\\
cot \ y -tan \ x= cot \ y -tan \ x [/tex]
