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Math Help - Prove(5)

  1. #1
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    Prove(5)

    Prove cos^2A-cos^2B=sin(B-A)sin(B+A)

    I attempted the question start with the RHS, using the addition formulae and ended off with cot^2A-cot^2B...
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  2. #2
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    Quote Originally Posted by Punch View Post
    Prove cos^2A-cos^2B=sin(B-A)sin(B+A)

    I attempted the question start with the RHS, using the addition formulae and ended off with cot^2A-cot^2B...
    lets start from the RHS .

    (\sin B\cos A-\cos B\sin A)(\sin B\cos A+\cos B\sin A)

    this is in the form of (a+b)(a-b)=a^2-b^2

    \sin^2 B\cos^2 A-\cos^2 B\sin^2 A

    (1-\cos^2 B)\cos^2 A-\cos^2 B(1-\cos^2 A)

    \cos^2 A-\cos^2 A\cos^2 B-\cos^2 B+\cos^2 B\cos^2 A
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