# weird trig question?

• Feb 23rd 2011, 07:00 PM
mathswannabe
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}
{\dfrac{1}{\sqrt{2}}}\left(\cos\theta-\sin\theta\right) &=&a\left(\cos\theta + \sin\theta\right)\nonumber
\end{eqnarray}
$

But don't know where to go from here??
• Feb 23rd 2011, 07:13 PM
Prove It
Are you sure it wasn't asking you to find $\displaystyle a$ if

$\displaystyle \cos{\left(\theta - \frac{\pi}{4}\right)} = a(\cos{\theta} + \sin{\theta})$?
• Feb 23rd 2011, 07:16 PM
harish21
Quote:

Originally Posted by mathswannabe
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}
{\dfrac{1}{\sqrt{2}}}\left(\cos\theta-\sin\theta\right) &=&a\left(\cos\theta + \sin\theta\right)\nonumber
\end{eqnarray}
$

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:

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