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Home » The eigenvalues are 5 and 2. - SUpost

The eigenvalues are 5 and 2. - SUpost

📅 July 5, 2026 👤 scraface

Jul 05, 2026

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Square both sides:
+ 2\sin z \cos z = 1 \Rightarrow 2\sin z \cos z = 0 \Rightarrow \sin 2...
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 \(\sin z + \cos z = 1\):
\(z = 0^\circ\): \(\sin 0 + \cos 0 = 0 + 1 = 1\) ✓
\(z = 90^\circ\): \(\sin 90 + \cos 90 = 1 + 0 = 1\) ✓
\(z = 180^\circ\): \(\sin 180 + \cos 180 = 0 - 1 = -1\) ✗
\(z = 270^\circ\): \(\sin 270 + \cos 270 = -1 + 0 = -1\) ✗
\(z = 360^\circ\): same as \(0^\circ\), so ✓

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