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Math Help - weird trig question?

  1. #1
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    weird trig question?

    Determine 'a' if

    \cos(\theta+{\frac{\pi}{4}}) = a(\cos\theta + \sin\theta)


    Using the identity:

    \cos(\theta+\phi)$ $=$ $\cos\theta\cdot\cos\phi-\sin\theta\cdot\sin\phi

    I have got
    \begin{eqnarray}<br />
{\dfrac{1}{\sqrt{2}}}\left(\cos\theta-\sin\theta\right) &=&a\left(\cos\theta + \sin\theta\right)\nonumber<br />
\end{eqnarray}<br />

    But don't know where to go from here??
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  2. #2
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    Are you sure it wasn't asking you to find \displaystyle a if

    \displaystyle \cos{\left(\theta - \frac{\pi}{4}\right)} = a(\cos{\theta} + \sin{\theta})?
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by mathswannabe View Post
    Determine 'a' if

    \cos(\theta+{\frac{\pi}{4}}) = a(\cos\theta + \sin\theta)


    Using the identity:

    \cos(\theta+\phi)$ $=$ $\cos\theta\cdot\cos\phi-\sin\theta\cdot\sin\phi

    I have got
    \begin{eqnarray}<br />
{\dfrac{1}{\sqrt{2}}}\left(\cos\theta-\sin\theta\right) &=&a\left(\cos\theta + \sin\theta\right)\nonumber<br />
\end{eqnarray}<br />

    But don't know where to go from here??
    \dfrac{1}{\sqrt{2}}(\cos(\theta)-\sin(\theta))=a(\cos(\theta)+\sin(\theta))

    a = \dfrac{1}{\sqrt{2}} \cdot \dfrac{(\cos(\theta)-\sin(\theta))}{(\cos(\theta)+\sin(\theta))}

    you can simplify further as:

    a =  \dfrac{1}{\sqrt{2}} \cdot \dfrac{(\cos(\theta)-\sin(\theta))}{(\cos(\theta)+\sin(\theta))} \times \dfrac{(\cos(\theta)+\sin(\theta))}{(\cos(\theta)+  \sin(\theta))}=...
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