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Math Help - Trigo-limit

  1. #1
    Super Member dhiab's Avatar
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    Trigo-limit

    Calculate :


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  2. #2
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    L'H˘pital's rule - Wikipedia, the free encyclopedia

    L'Hopitals Rule, should be useful.
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  3. #3
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     \frac{ \frac{\pi}{\sqrt{8}} - \sqrt{2} x \tan(x) }{ \sin(x) + \cos(x) }


     = \sqrt{2} ~ \frac{ \frac{\pi}{4} - x \tan(x) }{ \sin(x) + \cos(x) }


     =  \sqrt{2} ~ \frac{ \frac{\pi}{4} + x - x [ \tan(x) + 1 ]  }{ \sin(x) + \cos(x) }


     =  \sqrt{2} \left[ \frac{  \frac{\pi}{4} + x }{ \sqrt{2} \sin(  \frac{\pi}{4} + x) } - x~   \frac{\sin(x) + \cos(x) }{ \cos(x) [\sin(x) + \cos(x)] } \right]

     =  \frac{  \frac{\pi}{4} + x }{  \sin(  \frac{\pi}{4} + x)} - \frac{\sqrt{2} x}{\cos(x) }
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