Proof Using Trigonometry
We want to show it is always possible to solve
for




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(A.3) |
Applying this expansion to Eq.

![\begin{eqnarray*}
\left[A\cos(\phi)\right]\cos(\omega t)
&-&\left[A\sin(\phi)\ri...
...a t)
- \left[\sum_{i=1}^N A_i\sin(\phi_i)\right]\sin(\omega t).
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/filters/img1320.png)
Equating coefficients gives
where






which has a unique solution for any values of and
.
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Proof Using Complex Variables
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Half-Angle Tangent Identities