### Proof Using Trigonometry

We want to show it is always possible to solvefor and , given for . For each component sinusoid, we can write

(A.3) |

Applying this expansion to Eq.(A.2) yields

where and are known. We now have two equations in two unknowns which are readily solved by (1) squaring and adding both sides to eliminate , and (2) forming a ratio of both sides of Eq.(A.4) to eliminate . The results are

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Half-Angle Tangent Identities