Results 1 to 7 of 7
Like Tree3Thanks
  • 1 Post By yeongil
  • 2 Post By ibdutt

Thread: What would be the value?

  1. #1
    Newbie
    Joined
    Jun 2016
    From
    india
    Posts
    1

    Question What would be the value?

    hiiii,

    try to answer the simple trigonometry question.

    If A+B = 225 then what would be (1+tan A)(1+tan B) = ??

    Source:- If A+B = 225 then what would be (1+tan A)(1+tan B) = ??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    895
    Thanks
    200

    Re: What would be the value?

    Start with the expansion for tan(A+B) and see what you can do.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2016
    From
    USA
    Posts
    3

    Re: What would be the value?

    A+B=225
    A+B=180+45
    (1+tanA)(1+tanB)
    =(1+tan180)(1+tan45)
    =(1+0)(1+1)
    Ans. 2 [tan 180=0, tan45=1]
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    May 2009
    Posts
    612
    Thanks
    309

    Re: What would be the value?

    There are some problems here.

    1) Both abhik143 and garfieldmorse were naughty and did not include degree marks. Without degree marks, we are to assume that the angle is in radians. So
    tan 180 ≈ 2.339, not 0. (180 radians)
    tan 180 = 0. (180 degrees)

    2) Shouldn't the original question include the restriction that A ≠ 90 or B ≠ 90? Otherwise, (1 + tan A)(1 + tan B) can't be evaluated.

    3) I don't think that we can just say that A = 180 and B = 45. Let A = 100 and B = 125, for example, and you'll get the same answer for (1 + tan A)(1 + tan B).

    I think a better way to solve this would be to do the following:
    A + B = 225^{\circ}

    tan(A + B) = tan(225^{\circ})

    \frac{tan A + tan B}{1 - tan A \: tan B} = 1

    Multiply both sides by the denominator:

    tan A + tan B = 1 - tan A \: tan B

    tan A + tan B + tan A \: tan B = 1

    1 + tan A + tan B + tan A \: tan B = 2

    Factor the left side:

    (1 + tan A)(1 + tan B) = 2


    01
    Last edited by yeongil; Jul 19th 2016 at 04:49 AM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2016
    From
    kota
    Posts
    4

    Re: What would be the value?

    $(1+tanA)(1+tanB)=1+tanA+tanB+tanAtanB ........(1)$
    Given : $A+B=225$
    taking tan on both the sides
    $tan(A+B)=tan(225)$
    $tan(A+B)=tan(180+45)$
    $tan(A+B)=1 ........(2)$
    We know, $tan(A+B)=\dfrac{tanA+tanB}{1-tanAtanB}$
    put the value of tan(A+B) from equation (2)
    $1=\dfrac{tanA+tanB}{1-tanAtanB}$
    $1-tanAtanB=tanA+tanB$
    $1=tanA+tanB+tanAtanB ........(3)$
    put the value of $tanA+tanB+tanAtanB$ froam equation (3) into equation (1)
    $(1+tanA)(1+tanB)=1+1$
    Thus, $(1+tanA)(1+tanB)=2$
    Last edited by RajeshBhuria; Oct 3rd 2016 at 04:37 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    863
    Thanks
    220

    Re: What would be the value?

    It is better that we give hint / direction rather than spoon feeding in the interest of the learner
    Thanks from DenisB and topsquark
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Dec 2013
    From
    Colombia
    Posts
    1,839
    Thanks
    592

    Re: What would be the value?

    yeongil: Your point is perfectly valid, but for the question to make any sense (for it to be a well posed question) it cannot matter what choice we make for A and B, thus garfieldmorse's suggestion is perfectly justifiable with the condition "if an answer exists, it is 2".
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum