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Sign equality in proof of (sin A +sin B) trig identitiy

  1. Nov 19, 2013 #1
    1. The problem statement, all variables and given/known data
    To show that sin A + sin B = +2|sin ((A+B)/2)*cos((A-B)/2)| is easy. However, it is not clear how to remove the absolute value signs to give the valid identity sinA + sin B = 2(sin ((A+B)/2)*cos((A-B)/2)) without having to go through many cases.


    2. Relevant equations

    To prove the version with the absolute value is a straightforward application on the RHS of the half-angle identities and the angle addition/subtraction identities, whereupon one gets
    +√(sinA+sinB)2.


    3. The attempt at a solution
    I started with making a table of the different cases, some of which are straightforward. But the number of cases that must be examined gets to quickly be rather large, so I figure that there is an easier way to go about it. All help would be appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 19, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    I would prove it by adding sin(x+y) and sin(x-y) and then expanding them by addition formulas. Then put x=(A+B)/2 and y=(A-B)/2. Then the sign ambiguity never comes up.
     
  4. Nov 19, 2013 #3
    Thanks a million, Dick. Not only does the sign ambiguity never come up that way, but this is easier. Very elegant.
     
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