question_answer

If \[\tan \,\,\alpha =\frac{a}{b},\] where \[\alpha =12\beta \] and \[\alpha \] being an acute angle, then \[\frac{1}{2}\]\[[a\,\cos ec\,4\beta -b\,\sec \,4\beta ]\] is equal to ????.

A)  \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]       

B)  \[\sqrt{2\left( {{a}^{2}}+{{b}^{2}} \right)}\]

C)  \[\sqrt{2{{a}^{2}}+3{{b}^{2}}}\]                

D)  \[\sqrt{3{{a}^{2}}+2{{b}^{2}}}\]

E)  None of these