Vectors A→  and  B→  include  an  angle  θ  between  them.   If  (A→ +B→)  and  (A→−B→)  respectively subtend angles α and β with A, then (tanα+tanβ) is

tanα = BsinθA+Bcosθ ------(i)Where α is the angle made by the vector (A→ +B→)  with  A→Similarly, tanβ = BsinθA-Bcosθ   -------(ii)Where β is the angle made by the vector (A→ − B→)  with  A→Note that the angle between A→  and (− B→) is (1800)-θAdding (i) and (ii), we gettanα +tanβ = BsinθA+Bcosθ+BsinθA-Bcosθ =(AB sinθ −B2sinθcosθ+ABsinθ+B2sinθcosθ(A+Bcosθ)(A−Bcosθ)= 2ABsinθ(A2-B2cos2θ)