A) \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=1\]
B) \[\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}=1\]
C) \[\frac{1}{a}+\frac{1}{b}=1\]
D) \[\frac{1}{a}-\frac{1}{b}=1\]
Correct Answer: C
Solution :
\[\frac{1}{2}\,\left| \,\begin{matrix} a & 0 & 1 \\ 0 & b & 1 \\ 1 & 1 & 1 \\ \end{matrix}\, \right|=0\,\,\Rightarrow \,\,a\,(b-1)+0+1\,(-b)=0\] \[\Rightarrow \,\,ab-a-b=0\,\,\,\Rightarrow \,\,\frac{1}{a}+\frac{1}{b}=1\].
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