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Home » The perimeter of a rectangle is given by \( 2(\textlength + \textwidth) \). - Sterling Industries

The perimeter of a rectangle is given by \( 2(\textlength + \textwidth) \). - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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\sin x \cos x = \frac{1}{2} \sin(2x).
\frac{1}{\frac{1}{2} \sin(2x)} = 2\sqrt{2} \Rightarrow \frac{2}{\sin(2...
Now solve $ \sin(2x) = \frac{\sqrt{2}}{2} $ for $ x \in (0, \pi) $. Th...
The solutions to $ \sin \theta = \frac{\sqrt{2}}{2} $ in $ (0, 2\pi) $...
\theta = \frac{\pi}{4},\ \frac{3\pi}{4}.
So $ 2x = \frac{\pi}{4} \Rightarrow x = \frac{\pi}{8} $, and $ 2x = \f...
Both values lie in $ (0, \pi) $.
Therefore, the solutions are $ \boxed{\frac{\pi}{8},\ \frac{3\pi}{8}}...
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