pairing .. \[(1 + \tan x)(1 + \tan(\pi/4 - x)) = 2\]

We have the following relation: $(1+ \tan x)(1+ \tan (45-x))=2$, so by telescopic sum, we have $2^{22}(1+ \tan 45)$, since we can pair the tangents from 1 to 44 and $(1+\tan 45)$ remains by itself. Then, the result is $2^{22}(1+1)=2^{23}$, and the result follows.

parmenides51 wrote: Determine the value of the expression $$ (1 +\tan(1^o))(1 + \tan(2^o))...(1 + \tan(45^o)).$$ https://artofproblemsolving.com/community/c6h1709257p11014958