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 $$($$$$tan$$α$$+$$$$tan$$β$$)$$ is

Question

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 $$($$$$tan$$α$$+$$$$tan$$β$$)$$ is

Infinity Learn · Accepted Answer

$$tan$$α $$=$$ Bsinθ$$A+Bcos$$θ $$------(i)Where$$ α is the angle made by the vector (A$$→ $$+B$$→$$)  with  A→Similarly, $$tan$$β $$=$$ Bsinθ$$A-Bcos$$θ   $$-------(ii)Where$$ 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 $$+$$$$tan$$β $$=$$ Bsinθ$$A+Bcos$$θ$$+Bsin$$θ$$A-Bcos$$θ $$=(AB$$ $$sin$$θ −$$B2sin$$θ$$cos$$θ$$+ABsin$$θ$$+B2sin$$θ$$cos$$θ(A+Bcos$$θ$$)(A$$−Bcosθ$$)=$$ $$2ABsin$$θ$$(A2-B2cos2$$θ$$)

Vectors $\vec{A} a n d \vec{B} include an angle θ between them . If (\vec{A} + \vec{B}) and (\vec{A} - \vec{B}) respectively subtend angles α and β with A, then (tanα + tanβ) is$

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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

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Vectors $\vec{A} a n d \vec{B} include an angle θ between them . If (\vec{A} + \vec{B}) and (\vec{A} - \vec{B}) respectively subtend angles α and β with A, then (tanα + tanβ) is$