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Math Help - [SOLVED] Prove that this is true:

  1. #1
    Junior Member moonman's Avatar
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    [SOLVED] Prove that this is true:

    (sin0 - cos0)^(2) - cot0tan0 = -2sin0cos0

    *(all 0's = theta symbol)
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by moonman View Post
    (sin0 - cos0)^(2) - cot0tan0 = -2sin0cos0

    *(all 0's = theta symbol)
    Formula
    (a-b)^2 =a^2+b^2 -2ab


    Hence
    LHS=sin^2(\theta) +cos^2 (\theta) -2sin(\theta)cos(\theta)   - cot(\theta)\frac{1}{cot(\theta)}

     <br />
=1-2sin(\theta)cos(\theta) - 1 ...............(\text{using } sin^2x+ cos^2x=1)<br />

     <br />
 = RHS <br />
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  3. #3
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    Quote Originally Posted by moonman View Post
    (sin0 - cos0)^(2) - cot0tan0 = -2sin0cos0

    *(all 0's = theta symbol)
    1. You are supposed to know that

    \cot(\theta)=\dfrac1{\tan(\theta)}

    (\sin(\theta))^2+(\cos(\theta))^2 = 1

    2. Expand the bracket:

    (\sin(\theta))^2-2\cos(\theta) \cdot \sin(\theta)+(\cos(\theta))^2 - \dfrac1{\tan(\theta)} \cdot \tan(\theta) =

    Using the properties mentioned above you'll get:

    1 - 2\cos(\theta) \cdot \sin(\theta) -1 = -2\cos(\theta) \cdot \sin(\theta)


    EDIT: Too late ...
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