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Home » Solution: Rewrite $ \tan \theta + \cot \theta = 4 $ as: - 500apps

Solution: Rewrite $ \tan \theta + \cot \theta = 4 $ as: - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Ah — error in interpretation: in gravitational lensing, **larger mass** produces **larger deflection**, hence **larger apparent separation**.

📌 But the problem says: "scales with mass and inversely proportional to distance" — but if distance is same, then separation ∝ mass.

📌 But 0.8 < 1.6, so mass must be smaller — contradiction.

📌 Unless the 1.6 arcsec is for the nearby cluster? But it says "a nearby cluster... 1.6 arcseconds".

📌 Re-read: "a nearby cluster tallies a separation of 1.6 arcseconds at equal distance" — so same distance.

📌 But 0.8 < 1.6 → so mass must be less — but lensing is weaker. So smaller separation makes sense — weaker lensing.

📌 So the given separateion (0.8) corresponds to less mass? But the claim is scale with mass.

📌 Resolution: the proportionality is approximate, but the problem says "∝ mass / distance".

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