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angle = \langle -1, -2 - Fine VPN

📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 \sec \theta + \csc \theta = \frac{1}{\cos \theta} + \frac{1}{\sin \theta} = \frac{\sin \theta + \cos \theta}{\sin \theta \cos \theta}.

📌 The square is:

📌 Using the identity \((\sin \theta + \cos \theta)^2 = 1 + \sin 2\theta\), and \(\sin \theta \cos \theta = \frac{1}{2} \sin 2\theta\), we rewrite it as:

📌 Let \(y = \sin 2\theta\), where \(y \in (0, 1]\). Define:

📌 f(y) = \frac{4(1 + y)}{y^2}.

📌 To find the maximum of \(f(y)\) on \( (0,1] \), take the derivative:

📌 f'(y) = 4 \cdot \frac{(1)(y^2) - (1 + y)(2y)}{y^4} = 4 \cdot \frac{y^2 - 2y(1 + y)}{y^4} = 4 \cdot \frac{y^2 - 2y - 2y^2}{y^4} = 4 \cdot \frac{-y^2 - 2y}{y^4} = -4 \cdot \

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Actually: 3.14 × 49 = 153.86
× 1.8 = 276.948 → closest to 276.95, but format expects clean answer.
Wait — perhaps use π=22/7? No, specified 3.14.
But in final answer, compute numerically:
≈ 277.55? Wait: 153.86 × 1.8:
× 1.8 = 153.86 × (18/10) = (153.86 × 18) / 10
× 10 = 1,538.6 → ×1.8 = 1,538.6 × 0.8 = 1,230.88, plus 153.86 × 0.8 =...
= 18/10, so (153.86 × 18) / 10
× 10 = 1,538.6, ×1.8:
Better: 153.86 × 1.8 = 153.86 × (1 + 0.8) = 153.86 + 123.088 = 276.948

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