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Math Help - Proving Identies

  1. #1
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    Proving Identies

    How do I prove this identity. The only thing I know is that I have to use a product to sum formula, but which one?

    \frac{cos 66 * cos 6 + cos 84 * cos 24}{cos 65 * cos 5 + cos 85 * cos 25}=1
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  2. #2
    MHF Contributor
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    Quote Originally Posted by HSS8 View Post
    How do I prove this identity. The only thing I know is that I have to use a product to sum formula, but which one?

    \frac{cos 66 * cos 6 + cos 84 * cos 24}{cos 65 * cos 5 + cos 85 * cos 25}=1
    HI

    \frac{\frac{1}{2}[\cos 72+\cos 60]+\frac{1}{2}[\cos 108+\cos 60]}{\frac{1}{2}[\cos 70+\cos 60]+\frac{1}{2}[\cos 110+\cos 60]}

    =\frac{\frac{1}{2}[\cos 72+\cos 108+2\cos 60]}{\frac{1}{2}[\cos 70+\cos 110+2\cos 60]}

    =\frac{\frac{1}{2}[\cos 72+(-\cos 72)+2\cos 60]}{\frac{1}{2}[\cos 70+(-\cos 70)+2\cos 60]}

    so all these would cancel off to give you 1.
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  3. #3
    Senior Member pacman's Avatar
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    i thought only clues or a little help (not complete solution) will be given on the first day?

    ,

    we will use this: , yes cos(A - B), you will see the pattern once you apply it.

    Numerator = N = cos 66 cos 6 + cos 84 cos 24 = cos 66 cos 6 + sin 6 sin 66

    Denominator = D = cos 65 cos 5 + sin 5 sin 65

    N/D = ?
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