manitkapoor2
Answered

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

Sagot :

madankapoor10
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]
(1+tan 1)(1+ tan 2)...(1+tan 45)=(1+0.017455)(1+0.03492)...(1+1)=8388608.11
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