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Mar 01, 2026

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S = rac{2(e^{i heta} + e^{-i heta} + e^{i\phi} + e^{-i\phi})}{e^{i he...
This simplifies to $ rac{2(2\cos heta + 2\cos\phi)}{2i(\sin heta - \s...
S = rac{(a + b)^2 + (a - b)^2}{a^2 - b^2} = rac{2a^2 + 2b^2}{a^2 - b...
But $ a^2 - b^2 = (a - b)(a + b) $, and $ a^2 + b^2 = (a + b)^2 - 2ab...
S = rac{2(1 + (-1))}{1 - (-1)} = 0.
But earlier steps suggest $ S = rac{2(a^2 + b^2)}{a^2 - b^2} $. For $...
S = rac{2(e^{2i heta} + e^{2i\phi})}{e^{2i heta} - e^{2i\phi}} = 2 \c...
Multiply numerator and denominator by $ e^{-i( heta + \phi)/2} $:
S = 2i \cdot rac{e^{i( heta - \phi)/2} + e^{-i( heta - \phi)/2}}{e^{i...
ight)}{2i\sin\left(rac{ heta - \phi}{2}

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