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Math Help - cosine rule

  1. #1
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    cosine rule

    hi!

    can i know how to prove that the cosine rule is true for ∏/2≤ x ≤∏ for
    c^2 = a^2 + b^2 - 2ab cos x?

    i want to show that it is true for 0 ≤ x ≤∏ and have proven that it is true for 0≤x≤∏/2 but i dont know how to prove the other part..

    thanks!!!
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  2. #2
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    Hello alexandrabel90
    Quote Originally Posted by alexandrabel90 View Post
    hi!

    can i know how to prove that the cosine rule is true for ∏/2≤ x ≤∏ for
    c^2 = a^2 + b^2 - 2ab cos x?

    i want to show that it is true for 0 ≤ x ≤∏ and have proven that it is true for 0≤x≤∏/2 but i dont know how to prove the other part..

    thanks!!!
    In the attached diagram:

    c^2 = [a + b\cos(\pi-x)]^2+[b\sin(\pi-x)]^2

    =a^2+2ab\cos(\pi-x)+b^2\cos^2(\pi-x)+b^2\sin^2(\pi-x)

    Now \cos(\pi-x) = -\cos x and \sin(\pi-x) = \sin x. So \cos^2(\pi-x) = (-\cos x)^2 =\cos^2x

    \Rightarrow c^2 = a^2 -2ab\cos x + b^2(\cos^2x + \sin^2x)

    = a^2 +b^2 -2ab\cos x, since \cos^2x + \sin^2x = 1

    Grandad
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