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Homework Help: Obtaining the identity

  1. Aug 5, 2005 #1
    yes well I got the last problem.....but I still wanna have an idea were the identity siny+sinx=2sin(x+y)/2cos(x+y)/2 came from please someone sort of explain plz! thanx
     
  2. jcsd
  3. Aug 5, 2005 #2

    lurflurf

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    Homework Helper

    what you wrote is not an identity consider x=y=pi/2
    sin pi/2+sin pi/2=2
    2sin pi/2 cos pi/2=0
    do you mean
    [tex]\sin(y)+\sin(x)=2\cos(\frac{y-x}{2})\sin(\frac{y+x}{2})[/tex]
    if so
    start on the left by writing
    y=(y+x)/2+(y-x)/2
    x=(y+x)/2-(y-x)/2
    then expand using
    sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
    and
    sin(a-b)=sin(a)cos(b)-cos(a)sin(b)
    add like terms
     
    Last edited: Aug 5, 2005
  4. Aug 5, 2005 #3
    back to the root

    Dainy:

    Make sure that you understand why

    cos(a-b) = cos(a) cos(b) + sin(a) sin(b)

    and that you can illustrate the meaning of this formula with a drawing.

    Many other formulas can be derived form the previous by algebra and by other simple trigonometric rules (likes cos(-b)=cos(b), sin(-b)=-sin(b), cos(pi-b)=-cos(b), ... all rules that can be illustrated by a drawing too.).

    So the picture is: a few simple principles and definitions, enough algebra, and you are on your own.
     
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