A) 21
B) 22
C) 23
D) 24
Correct Answer: C
Solution :
If \[A+B={{45}^{o}}\] \[\Rightarrow \,\,(1+\tan A)\,(1+\tan B)=2\]. \[\therefore \] The given expression can be written as \[(1+\tan {{45}^{o}})\] \[\left\{ \begin{align} & ((1+\tan {{1}^{o}})(1+\tan {{44}^{o}}))((1+\tan {{2}^{o}})(1+\tan {{43}^{o}})) \\ & ....(1+\tan {{22}^{o}})(1+\tan {{23}^{o}}) \\ \end{align} \right\}={{2}^{n}}\]\[\Rightarrow \,2\left[ {{2}^{22}} \right]={{2}^{n}}\] \[\Rightarrow \,n=23\]
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