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Math Help - Prove trigonometric inequality?

  1. #1
    Super Member fardeen_gen's Avatar
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    Prove trigonometric inequality?

    Prove that:
    (\cot^2 x - 1)(3\cot^2 x - 1)(\cot 3x\cdot\tan 2x - 1)\leq -1
    is valid for all values of x for which the LHS is defined.
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  2. #2
    MHF Contributor red_dog's Avatar
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    \cot 3x=\frac{\cot^3x-3\cot x}{3\cot^2x-1}, \ \tan 2x=\frac{2\cot x}{\cot^2x-1}

    The inequality becomes

    -\cot^4x-2\cot^2x-1\leq -1 and this is true.
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