question_answer

If \[\text{Cosec}\,\alpha -\text{Sin}\,\alpha =a\] and \[\text{Sec}\,\alpha -\text{Cos}\,\alpha =b,\]then \[\left( {{\mathbf{a}}^{\mathbf{2}}}+\text{ }{{\mathbf{b}}^{\mathbf{2}}}+\text{ }\mathbf{3} \right)\] is equal to ___­­­­­­____

A)  \[\frac{1}{ab}\]                                                

B)  \[{{a}^{2}}+{{b}^{2}}\]        

C)  \[\frac{1}{{{a}^{2}}+{{b}^{2}}}\]       

D) \[{{a}^{2}}{{b}^{2}}+1\]

E) None of these