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Home » Question: Find the minimum value of $(\csc x + \cot x)^2 + (\sec x - an x)^2 - AMAZONAWS

Question: Find the minimum value of $(\csc x + \cot x)^2 + (\sec x - an x)^2 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 \boxed{\begin{pmatrix} 1 & 3 \\ 3 & 3 \end{pmatrix}}

📌 الإجابة النهائية:** $\boxed{\begin{pmatrix} 1 & 3 \\ 3 & 3 \end{pmatrix}}$

📌 السؤال: أوجد جميع الزوايا $z \in [0^\circ, 360^\circ]$ التي تحقق المعادلة $2\sin z + \sqrt{3} = 0$.

📌 2\sin z + \sqrt{3} = 0 \implies \sin z = -\frac{\sqrt{3}}{2}

📌 الزوايا $z$ التي تحقق $\sin z = -\frac{\sqrt{3}}{2}$ تقع في الربعين الثالث والرابع. الزاوية المرجعية هي $60^\circ$ لأن $\sin 60^\circ = \frac{\sqrt{3}}{2}$. لذلك، الحلول في الفترة $[0^\circ, 360^\circ]$ هي:

📌 z = 180^\circ + 60^\circ = 240^\circ \quad \text{و} \quad z = 360^\circ - 60^\circ = 300^\circ

📌 \boxed{240^\circ} \quad \text{و} \quad \boxed{300^\circ}

📌 الإجابة النهائية:** الزوايا هي $\boxed{240^\circ}$ و $\boxed{300^\circ}$.

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