Question

(1+tan1)(1+tan2)................(1+tan45)?

Answer 1

if a+b=45 then (1+tan(a) )( 1+ tan(b) )=2
tan(b)=tan(45-a) =2 cos(a)/(cos(a)+sin(a))-1
1+tan(b)=2 cos(a)/(cos(a)+sin(a))
tan(a)=sin(a)/cos(a)
1+tan(a)=1+sin(a)/cos(a)=(sin(a)+cos(a))/cos(a)
(1+tan(a) )( 1+tan(b) )=[ (sin(a)+cos(a))/cos(a) ]*[2cos(a)/(cos(a)+sin(a))]=2
(1+tan1)(1+tan2)................(1+tan45)=[(1+tan1)(1+tan44) ]*[ (1+tan 2)(1+tan43) ]*...*[(1+tan22)(1+tan23)] *(1+tan
45)=2^(22) * (1+tan 45)=2^23