Results 1 to 2 of 2

Math Help - help

  1. #1
    Member
    Joined
    Dec 2008
    Posts
    154

    help

    prove |x-y|>= |sin x - sin y|

    please help on this.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    For x=y, there's nothing to prove.

    Assume x\ne y and by the MVT applied to f(t)=\sin t,\,\exists\,\varphi\in(x,y) then, \frac{\sin x-\sin y}{x-y}=\cos \varphi \implies \left| \sin x-\sin y \right|=\left| x-y \right|\left| \cos \varphi  \right|.

    It remains a simple little step to solve this, I let you to figure out.
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum