If $(1+\tan 1°)(1+\tan 2°)\mathrm{.........}$$(1+\tan 45°)=2^n$ then $n=$

$\begin{array}{l}\left(1+\tan 1^{\circ }\right)\left(1+\tan 2^{\circ }\right)\dots ..\left(1+\tan {44}^{\circ }\right)\\ \left(1+\tan {45}^{\circ }\right)=2^n\\ \left(\because A+B={45}^{\circ }\Rightarrow (1+\tan A)(1+\tan B)=2\right)\\ =2.2\dots .2\left(22\text{ times }\right)(1+1)=2^n\\ \Rightarrow 2^{22}\left(2\right)=2^n\\ \Rightarrow 2^{23}=2^n\\ \therefore n=23\end{array}$