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Math Help - number identity

  1. #1
    Senior Member pacman's Avatar
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    number identity

    what is the value of this number identity?

    (sec 11)(sec 19) - (2 cot 71) = ?






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  2. #2
    Super Member Matt Westwood's Avatar
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    Degrees or radians?
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  3. #3
    Senior Member pacman's Avatar
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    Matt, it is degrees. I am too lazy to learn LATEX. Sorry for the mishap . . . .

    i wonder what trigonometric identity generated this strange number.
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  4. #4
    MHF Contributor
    Grandad's Avatar
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    Hello pacman
    Quote Originally Posted by pacman View Post
    what is the value of this number identity?

    (sec 11)(sec 19) - (2 cot 71) = ?
    I haven't an exact answer, but a simplification of the expression, as follows:

    \sec11\sec19-2\cot71 = \frac{1}{\cos11\cos19}-2\frac{\cos71}{\sin71}

    = \frac{1}{\cos11\cos19}-2\frac{\cos71}{\cos19}, since \sin A = \cos(90-A)

    =\frac{1-2\cos71\cos11}{\cos11\cos19}

    =\frac{1-(\cos82+\cos60)}{\cos11\cos19}, using 2\cos A \cos B = \cos(A+B)+\cos(A-B)

    =\frac{0.5-\cos82}{\cos11\cos19}

    =\frac{\sin30-\sin8}{\cos11\cos19}

    =\frac{2\cos19\sin11}{\cos11\cos19}, using \sin A - \sin B = 2\cos\tfrac12(A+B)\sin\tfrac12(A-B)

    =2\tan11

    I don't think you can go any further in terms of a numerical value.

    Grandad
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  5. #5
    Senior Member pacman's Avatar
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    thanks GRANDAD! this is the simplification i wanted to have.
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