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Math Help - Math question

  1. #1
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    Math question

    Hi.Can any one help me with these questions.They are really simple but i cannot seem to get them.Thanks
    Q1.Show That:


    Q2.Prove that:


    Q3.Prove that:


    Thanks a lot.
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  2. #2
    Member srirahulan's Avatar
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    Re: Math question

    Hi,
    I think Tan(270-\theta)=Cot\theta
    L.H.S
    = tan(270-x)
    = \frac{sin(270-\theta}{cos(270-\theta)}
    = \frac{sin270cos\theta-cos270sin\theta}{cos270cos\theat+sin270sin\theta}
    = \frac{-cos\theta-0}{0-sin\theta}
    = \frac{cos\theta}{sin\theta}
    = cot\theta


    In your Q2
    cos(\alpha+\beta)cos(\alpha-\beta)=cos^2\alpha-sin^2\beta=cos^2\beta-sin^2\alpha

    Take L.H.S

    = \frac{cos(\alpha+\beta)cos(\alpha-\beta)}{1}
    multiply by 2

    = \frac{2cos(\alpha+\beta)cos(\alpha-\beta)}{2}
    = \frac{cos2\alpha+cos2\beta}{2}
    = \frac{2cos^2\alpha+2Cos^2\beta-2}{2}
    = cos^2\alpha+cos^2\beta-1
    = cos^2\alpha-(1-cos^2\beta)
    = cos^2\alpha-sin^2\beta
    Or
    = cos^2\beta-(1-cos^2\alpha)
    = cos^2\beta-sin^2\alpha

    In Your Q3

    I think you have a mistake,I think the answer will be -cos\theta
    Last edited by srirahulan; July 30th 2012 at 07:18 PM.
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  3. #3
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    Re: Math question

    Thanks a lot for the help.

    BTW,can you tell me of a good equation writing software?

    Thanks again.
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  4. #4
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    Re: Math question

    Quote Originally Posted by hacker804 View Post
    Hi.Can any one help me with these questions.They are really simple but i cannot seem to get them.Thanks
    Q1.Show That:


    Q2.Prove that:


    Q3.Prove that:


    Thanks a lot.
    It's easier in Q.1 to do

    \displaystyle \begin{align*} \tan{\left(270^{\circ} - \theta\right)} &= \tan{\left(180^{\circ} + 90^{\circ} - \theta\right)} \\ &= \tan{\left(90^{\circ} - \theta\right)} \\ &= \frac{\sin{\left(90^{\circ} - \theta\right)}}{\cos{\left(90^{\circ} - \theta\right)}} \\ &= \frac{\cos{\theta}}{\sin{\theta}} \\ &= \cot{\theta} \end{align*}
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  5. #5
    Member srirahulan's Avatar
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    Re: Math question

    Good Idea.Nice work.
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  6. #6
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    Re: Math question

    Thanks for all the help
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