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Math Help - TRigo Prov. Identities

  1. #1
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    Question TRigo Prov. Identities

    Number 2 involves many angles:

    #1 (cos X) / (cos X - sin X) = (cot X) / (cot X -1)


    #2 (sin 3X + sin 7X) / (cos 7X + cos 3X) = tan 5X
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  2. #2
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    Quote Originally Posted by olokish View Post
    Number 2 involves many angles:

    #1 (cos X) / (cos X - sin X) = (cot X) / (cot X -1)


    #2 (sin 3X + sin 7X) / (cos 7X + cos 3X) = tan 5X

    1. \frac{\cot{x}}{\cot{x} - 1} = \frac{\frac{\cos{x}}{\sin{x}}}{\frac{\cos{x}}{\sin  {x}} - 1}

     = \frac{\frac{\cos{x}}{\sin{x}}}{\frac{\cos{x} - \sin{x}}{\sin{x}}}

     = \frac{\cos{x}\sin{x}}{\sin{x}(\cos{x} - \sin{x})}

     = \frac{\cos{x}}{\cos{x} - \sin{x}}.
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