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Math Help - trig help for vector calc class

  1. #1
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    Question trig help for vector calc class

    A= A(cosx)^2 + 2Bcosxsinx + C(sinx)^2
    C= A(sinx)^2 2Bcosxsinx + C(cosx)^2


    I need to prove that (A)(C) is equal to AC B^2

    If tried multiplying both together but I cant seem to find the right trig identities or how to simplify it.
    any steps or hints would be Great
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  2. #2
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    Quote Originally Posted by lauren2988 View Post
    A= A(cosx)^2 + 2Bcosxsinx + C(sinx)^2
    C= A(sinx)^2 2Bcosxsinx + C(cosx)^2


    I need to prove that (A)(C) is equal to AC B^2

    If tried multiplying both together but I cant seem to find the right trig identities or how to simplify it.
    any steps or hints would be Great
    I believe that there is something missing here, and that the correct identity should be A'C'-B'^2 = AC-B^2, where B' = -A\sin x\cos x + B(\cos^2x-\sin^2x) + C\sin x\cos x.

    To prove it, check that \begin{bmatrix}A'&B'\\B'&C'\end{bmatrix} = \begin{bmatrix}\phantom{-}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix} \begin{bmatrix}A&B\\B&C\end{bmatrix} \begin{bmatrix}\cos x&-\sin x\\\sin x&\phantom{-}\cos x\end{bmatrix}, and take the determinant of both sides.
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