manitkapoor2
Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.