question_answer

If m Cot \[\theta \] + n Cosec\[\theta \] = a and n Cot \[\theta \] + m Cosec\[\theta \] = b, then \[{{\mathbf{a}}^{\mathbf{2}}}-\text{ }{{\mathbf{b}}^{\mathbf{2}}}\] is equal to _______

A)  \[{{n}^{2}}-{{m}^{2}}\]                              

B)  \[{{m}^{2}}+\text{ }{{n}^{2}}\]      

C)  \[{{m}^{2}}-{{n}^{2}}\]                                                                  

D) \[{{\left( m-n \right)}^{2}}\]

E) None of these