2008
Problem - 2288
Compute $(1+\tan 1^\circ)(1+\tan 2^\circ)\cdots(1+\tan 44^\circ)(1+\tan 45^\circ)$
Note that
$$(1+\tan\alpha)(1+\tan(45^\circ - \alpha))=(1+\tan\alpha)\Big(1+\frac{\tan 45^\circ - \tan\alpha}{1+\tan 45^\circ \tan\alpha}\Big)=2$$
We find the original expression equals $\boxed{2^{22}}$.