manitkapoor2
Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.