question_answer

If \[\mathbf{tanA}=\mathbf{n}\,\mathbf{tanB}\]and\[\mathbf{sin}\text{ }\mathbf{A}=\mathbf{n}\text{ }\mathbf{sinB}\], then find the value of\[\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{A}\].

A) \[\frac{{{m}^{2}}+1}{{{n}^{2}}+1}\]         

B) \[\frac{{{m}^{2}}+1}{{{n}^{2}}-1}\]

C) \[\frac{{{m}^{2}}-1}{{{n}^{2}}+1}\]           

D) \[\frac{{{m}^{2}}-1}{{{n}^{2}}-1}\]

E) None of these