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Home » 4x^2 + 50x + 150 = 231 - Dyverse

4x^2 + 50x + 150 = 231 - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Find the sum of all angles \(z \in [0^\circ, 360^\circ]\) that satisfy \(\sin z + \cos z = 1\).

📌 We solve \(\sin z + \cos z = 1\) for \(z \in [0^\circ, 360^\circ]\).

📌 Square both sides:

📌 + 2\sin z \cos z = 1 \Rightarrow 2\sin z \cos z = 0 \Rightarrow \sin 2z = 0

📌 So, \(2z = 0^\circ, 180^\circ, 360^\circ, 540^\circ, \ldots\), giving:

📌 z = 0^\circ, 90^\circ, 180^\circ, 270^\circ, 360^\circ

📌 Now check which satisfy the original equation \(\sin z + \cos z = 1\):

📌 \(z = 0^\circ\): \(\sin 0 + \cos 0 = 0 + 1 = 1\) ✓

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