Results 1 to 3 of 3

Math Help - (1+tan 1)(1+tan 2).....(1+tan 45)=

  1. #1
    Newbie
    Joined
    Oct 2011
    Posts
    3

    (1+tan 1)(1+tan 2).....(1+tan 45)=

    (1+tan 1)(1+tan 2).....(1+tan 45)=

    What should i be knowing to find the answer to this ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7

    Re: (1+tan 1)(1+tan 2).....(1+tan 45)=

    Quote Originally Posted by Raj917 View Post
    (1+tan 1)(1+tan 2).....(1+tan 45)=

    What should i be knowing to find the answer to this ?
    First, you can write it as (1+\tan 0^\circ)(1+\tan 1^\circ)(1+\tan 2^\circ)\cdots(1+\tan 45^\circ) (because the additional term at the beginning is equal to 1).

    Next, pair off the terms from the beginning and the end:

    \bigl((1+\tan 0^\circ)(1+\tan 45^\circ)\bigr) \bigl((1+\tan 1^\circ)(1+\tan 44^\circ)\bigr)\cdots\bigl((1+\tan 22^\circ)(1+\tan 23^\circ)\bigr).

    Then see if you can work out the value of each of those paired products.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2011
    Posts
    3

    Re: (1+tan 1)(1+tan 2).....(1+tan 45)=

    Quote Originally Posted by Opalg View Post
    First, you can write it as (1+\tan 0^\circ)(1+\tan 1^\circ)(1+\tan 2^\circ)\cdots(1+\tan 45^\circ) (because the additional term at the beginning is equal to 1).

    Next, pair off the terms from the beginning and the end:

    \bigl((1+\tan 0^\circ)(1+\tan 45^\circ)\bigr) \bigl((1+\tan 1^\circ)(1+\tan 44^\circ)\bigr)\cdots\bigl((1+\tan 22^\circ)(1+\tan 23^\circ)\bigr).

    Then see if you can work out the value of each of those paired products.

    Thank you sir the answer is 2^23
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum