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📅 May 17, 2026 👤 scraface

May 17, 2026

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\sin(2z) + \sqrt{3} \cos(2z) = 1
We rewrite the left-hand side as a single sine function. Let:
R \sin(2z + \alpha) = \sin(2z) + \sqrt{3} \cos(2z)
R \left( \sin(2z)\cos\alpha + \cos(2z)\sin\alpha \right) = R \cos\alph...
Matching coefficients:
R \cos\alpha = 1, \quad R \sin\alpha = \sqrt{3}
R^2 = 1^2 + (\sqrt{3})^2 = 4 \Rightarrow R = 2
\cos\alpha = \frac{1}{2}, \quad \sin\alpha = \frac{\sqrt{3}}{2} \Right...
So the equation becomes:
\sin(2z + 60^\circ) = 1 \Rightarrow \sin(2z + 60^\circ) = \frac{1}{2}

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