Question

IMPOSSIBLE MATH QUESTION

(1+tan (1))(1+tan (2))(1+tan (3))(1+tan (4))...(1+tan (45))=?
find the value

Answer 1

(1+tan 1)(1+ tan 2)...(1+tan 45)=(1+0.017455)(1+0.03492)...(1+1)=8388608.11

Answer 2

well u can also do this without a calculator
take
`tan 1=tan(45-44)=(1-tan44)/(1+tan 44)`
then

`(1+tan1)=(1+ (1-tan44)/(1+tan 44))=(2)/(1+tan 44)`
therefore similarly

`(1+tan 1)(1+tan 2)...(1+tan 22)= (2)/(1+tan 44) (2)/(1+tan 43)(2)/(1+tan 42)..(2)/(1+tan 23)`

`= (2^(22))/((1+tan 44)(1+tan 43)(1+tan 42)...(1+tan 23))`
then
`(1+tan 1)...(1+tan 45)= (2^(22))/((1+tan 44)(1+tan 43)(1+tan 42)...(1+tan 23))(1+tan 23)(1+tan 24)...(1+tan 45)`

`=2^(22)(1+tan45)=2^(23)=8388608`