A) 3
B) 4
C) 5
D) 6
Correct Answer: D
Solution :
For y to the real \[-1\le {{\tan }^{-1}}\,x\le 1\] \[\begin{align} & \Rightarrow \,\,-\tan \,1\le x\le \tan 1 \\ & \,\,\,\,\,\,\,\,y=\sqrt{\operatorname{t}+1}\,\,+\sqrt{1-t} \\ \end{align}\] \[\Rightarrow \,\,{{y}^{2}}=2+2\sqrt{1-{{t}^{2}}}\] \[\Rightarrow \,\,\,{{y}^{2}}\,\in \,[2,4]\] \[\Rightarrow \,\,\,y\in \left[ \sqrt{2},\,\,2 \right]\] \[\Rightarrow \,\,({{a}^{2}}+{{b}^{2}})=6\]
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