Please Help. Establish Identity: sin(x+y)/tan(x)+tan(y)= cos(x)cos(y)

Question

Please Help. Establish Identity: sin(x+y)/tan(x)+tan(y)= cos(x)cos(y)

Answer 1

To solve this identity you have to mean: sin(x+y)/(tan(x) +tan(y))=cos(x)cos(y)

 

first of all sin(x+y)=cos(x)sin(y)+cos(y)sin(x)

 

secondly tan(x)+tan(y)=(sin(x)/cos(x))+(sin(y)/cos(y))=(sin(x)cos(y)+sin(y)cos(x))/cos(x)cos(y)

 

so we have: (cos(x)sin(y)+cos(y)sin(x))/(sin(x)cos(y)+sin(y)cos(x))/cos(x)cos(y) which is equal to cos(x)cos(y)