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Home » 2\sin^2 z - 3\sin z + 1 = 0 - Silent Sales Machine

2\sin^2 z - 3\sin z + 1 = 0 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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ight) - 2 \geq 2 - 2 = 0,
with equality only if $ rac{p+q}{p-q} = rac{p-q}{p+q} $, which impli...
R = rac{x + 1}{x - 1} + rac{x - 1}{x + 1} - 2.
Let $ f(x) = rac{x+1}{x-1} + rac{x-1}{x+1} - 2 $. Combine:
f(x) = rac{(x+1)^2 + (x-1)^2}{(x-1)(x+1)} - 2 = rac{2x^2 + 2}{x^2 -...
ight) = 2\left( rac{2}{x^2 - 1}
ight) = rac{4}{x^2 - 1}.
Since $ x > 1 $, $ x^2 - 1 > 0 $, so $ f(x) > 0 $, and as $ x o 1^+ $...
rac{a}{b} + rac{b}{a} - 2 \geq 0,
with equality only if $ a = b $, i.e., $ rac{p+q}{p-q} = rac{p-q}{p+...

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