question_answer

If \[x=\text{a sec}\theta +\text{b tan}\theta \] and\[\text{y}=\text{b sec}\theta +\text{a tan}\theta \], find\[{{x}^{2}}-{{y}^{2}}\].

A)  \[4ab\,\sec \theta +a\tan \theta \]

B)         \[{{a}^{2}}-{{b}^{2}}\]

C)  \[{{b}^{2}}-{{a}^{2}}\]  

D)         \[{{a}^{2}}+{{b}^{2}}\]