question_answer

Vectors \[\overrightarrow{a}\] and \[\overrightarrow{b}\] include an angle \[\theta \] between them. If \[\left( \overrightarrow{a}+\overrightarrow{b} \right)\] and \[\left( \overrightarrow{a}-\overrightarrow{b} \right)\] respectively subtend angles \[\alpha \] and \[\beta \] with \[\overrightarrow{a}\] then \[\left( \tan \alpha +\tan \beta  \right)\]is )

A) \[\frac{(absin\theta )}{\left( {{a}^{2}}+{{b}^{2}}{{\cos }^{2}}\theta  \right)}\]

B) \[\frac{(2absin\theta )}{\left( {{a}^{2}}-{{b}^{2}}{{\cos }^{2}}\theta  \right)}\]

C) \[\frac{({{a}^{2}}si{{n}^{2}}\theta )}{({{a}^{2}}+{{b}^{2}}{{\cos }^{2}}\theta )}\]

D) \[\frac{({{b}^{2}}si{{n}^{2}}\theta )}{({{a}^{2}}-{{b}^{2}}{{\cos }^{2}}\theta )}\]