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Math Help - Proving a conditional indentity

  1. #1
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    Proving a conditional indentity

    Please see the attached image.
    I need to prove a conditional identity cosA + cosB + cosC = 1 + 4sin(A/2) + sin(B/2) + sin(C/2)
    given that A+B+C=pi. But the negative sign at the last is giving me trouble.
    Attached Thumbnails Attached Thumbnails Proving a conditional indentity-scan0001.jpg  
    Last edited by AaPa; July 3rd 2013 at 06:46 AM.
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  2. #2
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    Re: Proving a conditional indentity

    Your mistake is on your second line.

    \cos \left(\frac{A+B}{2}\right) is not equal to -\cos\left(\frac{C}{2}\right).
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  3. #3
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    Re: Proving a conditional indentity

    how?
    cos[(A+B)/2]
    =cos[(pi - c )/2]
    = -cos (c/2)
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  4. #4
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    Re: Proving a conditional indentity

    \frac{\pi - C}{2}=\frac{\pi}{2}-\frac{C}{2}.
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  5. #5
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    Re: Proving a conditional indentity

    yes I know that but A+B+C=pi

    so A+B=pi-c
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  6. #6
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    Re: Proving a conditional indentity

    !!!!!!!

    Expand \cos\left(\frac{\pi}{2}-\frac{C}{2}\right).
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  7. #7
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    Re: Proving a conditional indentity

    i know that it is equal to sin(c/2) but i want to write it in the form of cos.
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  8. #8
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    Re: Proving a conditional indentity

    Well, sin(c/2) is certainly NOT equal to -cos(c/2)!
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  9. #9
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    Re: Proving a conditional indentity

    You can't without introducing a square root, instead replace the \cos ^{2}\left(\frac{C}{2}\right) by 1-\sin ^{2}\left(\frac{C}{2}\right).
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  10. #10
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    Re: Proving a conditional indentity

    cos[(pi-c)/2]
    =cos(-c/2)
    =-cos(c/2)

    at which step am I wrong?
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  11. #11
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    Re: Proving a conditional indentity

    The second line is wrong.
    Read again posts 4 and 6.
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  12. #12
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    Re: Proving a conditional indentity

    Okay i got it.

    thanks.
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  13. #13
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    Re: Proving a conditional indentity

    Proving a conditional indentity-04-jul-13-2.png
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