Answer:[tex]\frac{cos(x-y)}{sin(x+y)}=\frac{1+cot(x)cot(y)}{cot(x)+cot(y)}[/tex][tex]Left\ side = Right\ side[/tex], hence the identity is verified.Step-by-step explanation:[tex]\frac{cos(x-y)}{sin(x+y}=\frac{1+cot(x)cot(y)}{cot(x)+cot(y)}[/tex]Working on right hand side.[tex]\frac{1+cot(x)cot(y)}{cot(x)+cot(y)}[/tex]Substituting [tex][cot(x)=\frac{cos(x)}{sin(x)}][/tex] and [tex][cot(y)=\frac{cos(y)}{sin(y)}][/tex] [tex]=\frac{1+\frac{cos(x)cos(y)}{sin(x)sin(y)}}{\frac{cos(x)}{sin(x)}+\frac{cos(y)}{sin(y)}}[/tex]Taking LCD and adding fractions.[tex]=\frac{\frac{sin(x)sin(y)+cos(x)cos(y)}{sin(x)sin(y)}}{\frac{cos(x)sin(y)+sin(x)cos(y)}{sin(x)sin(y)}}[/tex]Cancelling out the common denominators.[tex]=\frac{sin(x)sin(y)+cos(x)cos(y)}{cos(x)sin(y)+sin(x)cos(y)}}[/tex]Applying sum and difference formulas [tex][cos(x-y)=cos(x)cos(y)-sin(x)sin(y)][sin(x+y)=sin(x)cos(y)+sin(y)cos(x)][/tex][tex]=\frac{cos(x-y)}{sin(x+y)}[/tex]Left side[tex]\frac{cos(x-y)}{sin(x+y)}[/tex]∵ [tex]Left\ side = Right\ side[/tex], hence the identity is verified.