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Math Help - cotangent identity problem

  1. #1
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    cotangent identity problem

    Honestly, I'm not even sure how to start..

    Show: \frac{2cotx}{cot^2 + 1} = sin2x

    Thanks for your help, guys.
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  2. #2
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    Note the identity cot^{2}(x)+1=csc^{2}(x)

    \frac{2cot(x)}{cot^{2}(x)+1}=\frac{2\frac{cos(x)}{  sin(x)}}{csc^{2}(x)}=\frac{2\frac{cos(x)}{sin(x)}}  {\frac{1}{sin^{2}(x)}}

    =\frac{2cos(x)}{sin(x)}\cdot \frac{sin^{2}(x)}{1}=2cos(x)sin(x)=sin(2x)
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  3. #3
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    Quote Originally Posted by Savior_Self View Post
    Honestly, I'm not even sure how to start..

    Show: \frac{2cotx}{cot^2 + 1} = sin2x

    Thanks for your help, guys.
    \frac{2cot(x)}{cot^2(x) + 1}= \frac{2\frac{1}{\tan(x)}}{\frac{1}{\tan^2(x)}+1}= \frac{2\frac{\cos(x)}{\sin(x)}}{\frac{\cos^2(x)}{\  sin^2(x)}+1}= \frac{2\frac{\cos(x)}{\sin(x)}}{\frac{\cos^2(x)+\s  in^2(x)}{\sin^2(x)}}= \frac{2\frac{\cos(x)}{\sin(x)}}{\frac{1}{\sin^2(x)  }}= 2\frac{\cos(x)}{\sin(x)}\times\sin^2(x)=2\cos(x)\s  in(x)=\sin(2x).
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  4. #4
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    Quote Originally Posted by galactus View Post
    Note the identity cot^{2}(x)+1=csc^{2}(x)

    \frac{2cot(x)}{cot^{2}(x)+1}=\frac{2\frac{cos(x)}{  sin(x)}}{csc^{2}(x)}=\frac{2\frac{cos(x)}{sin(x)}}  {\frac{1}{sin^{2}(x)}}

    =\frac{2cos(x)}{sin(x)}\cdot \frac{sin^{2}(x)}{1}=2cos(x)sin(x)=sin(2x)
    err i think i chose the hard way.
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