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Math Help - supplementary exercise of trigo

  1. #1
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    supplementary exercise of trigo

    If A, B, C are the angles of a triangle, prove that cos2A + cos2B + cos2 C = 1-2cosAcosBcosC

    I've tried to use A+B+C=180, but I can't get the cos2 separately..
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  2. #2
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    Re: supplementary exercise of trigo

    this will help u
    it is done for A+B=C
    if A+B=C then prove that cos2A+cos2B + cos2C=1+2cosAcosB cos

    it is ur task to do the same for a+b+c=180(method used will be identical)
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  3. #3
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    Re: supplementary exercise of trigo

    Quote Originally Posted by mpx86 View Post
    this will help u
    it is done for A+B=C
    if A+B=C then prove that cos2A+cos2B + cos2C=1+2cosAcosB cos

    it is ur task to do the same for a+b+c=180(method used will be identical)
    why cos2A+cos2B= 2cos(A+B)cos(A-B) ?
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  4. #4
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    Re: supplementary exercise of trigo

    [sin ( Q+ β) + sin (Q − β)] = sin Q cos β,
    so that
    sin ( Q+ β) + sin ( Q− β) = 2 sin Q cos β. . . . . . (1)
    Now put
    Q + β = A
    and
    Q− β = B. . . . . . . . . . . . . . . .(2)
    The left-hand side of line (1) then becomes
    sin A + sin B.
    This is now the left-hand side of (e), which is what we are trying to prove.
    To complete the right−hand side of line (1), solve those simultaneous equations (2) for Q and β.
    On adding them, 2Q = A + B,
    so that
    Q = (A + B).
    On subtracting those two equations, 2β = A − B,
    so that
    β = (A − B).
    On the right−hand side of line (1), substitute those expressions for and β. Line (1) then becomes
    sin A + sin B = 2 sin (A + B) cos (A − B).

    HERE A=2C AND B=2D
    SUCH THAT sin 2C + sin 2D = 2 sin(C + D) cos (C − D).

    IT IS YOUR TASK TO PROVE TH SAME FOR ADDITION OF 2 COSINES....
    Thanks from Trefoil2727
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