Question 799186
Use the following trig identities:

sin(A+B) = sin(A)cos(B) + cos(A)sin(B)

tan(A) = sin(A)/cos(A)

tan(B) = sin(B)/cos(B)

Substitute the above into your equation and simplify the left side to look like the right side.

sin (A + B) = (sin A)(cos B) + (cos A)(sin B) ; Divide both sides by (cos A)(cos B)
=> sin (A + B) / {(cos A)(cos B)} = (sin A)/(cos A) + (sin B)/(cos B)
=> sin (A + B) / {(cos A)(cos B)} = tan A + tan B
=> sin (A + B) / (tan A + tan B) = (cos A)(cos B)

Verify your question.

Question for you:

 Is the denominator of LHS (tan A) + tan B) or (tan A)(tan B)? You did not make this clear in your post.