well u can also do this without a calculator
take [tex]tan 1=tan(45-44)=\frac{1-tan44}{1+tan 44} [/tex]
then
[tex](1+tan1)=(1+ \frac{1-tan44}{1+tan 44})=\frac{2}{1+tan 44}[/tex]
therefore similarly
[tex](1+tan 1)(1+tan 2)...(1+tan 22)= \frac{2}{1+tan 44} \frac{2}{1+tan 43}\frac{2}{1+tan 42}..\frac{2}{1+tan 23}[/tex]
[tex]= \frac{2^{22}}{(1+tan 44)(1+tan 43)(1+tan 42)...(1+tan 23)} [/tex]
then [tex](1+tan 1)...(1+tan 45)= \frac{2^{22}}{(1+tan 44)(1+tan 43)(1+tan 42)...(1+tan 23)}(1+tan 23)(1+tan 24)...(1+tan 45) [/tex]
[tex]=2^{22}(1+tan45)=2^{23}=8388608[/tex]
