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Math Help - Trig identity

  1. #1
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    Trig problem

    Solve for x\in R:

     <br />
\sin^{3}{x}(1+\cot{x})+\cos^{3}{x}(1+\tan{x})=\cos  {2x}<br />
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  2. #2
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    Quote Originally Posted by Sakai View Post
    Solve for x\in R:

     <br />
\sin^{3}{x}(1+\cot{x})+\cos^{3}{x}(1+\tan{x})=\cos  {2x}<br />
    \sin^{3}{x}(1+\cot{x})+\cos^{3}{x}(1+\tan{x}) = \cos^{2}{x} - \sin^{2}{x}

    \sin^{3}{x}+ \sin^{3}{x}\cot{x} + \cos^{3}{x} +\cos^{3}{x}\tan{x}= \cos^{2}{x} - \sin^{2}{x}

    \sin^{3}{x} + \cos^{3}{x} + \sin^{3}{x}\frac{\cos{x}}{\sin{x}} + \cos^{3}{x}\frac{\sin{x}}{\cos{x}}= \cos^{2}{x} - \sin^{2}{x}

    Now factorize and simplify.
    Last edited by sa-ri-ga-ma; May 31st 2010 at 06:06 PM.
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