1. ## weird trig question?

Determine 'a' if

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

Using the identity:

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

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

But don't know where to go from here??

2. Are you sure it wasn't asking you to find $\displaystyle \displaystyle a$ if

$\displaystyle \displaystyle \cos{\left(\theta - \frac{\pi}{4}\right)} = a(\cos{\theta} + \sin{\theta})$?

3. Originally Posted by mathswannabe
Determine 'a' if

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

Using the identity:

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

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

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

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

you can simplify further as:

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