Value of 36(4cos²9°-1)(4cos²27°-1)(4cos²81°-1)(4cos²243°-1)
A JEE Main 2023 trigonometric product that telescopes to a single value once each factor is rewritten using the sin 3θ triple-angle identity.
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Two Ellipses, Eccentricity 1/√3: Area of Quadrilateral ABCD
Two ellipses with the same eccentricity, a given latus rectum product, and a known focal distance intersect at four points. A JEE Main 2025 area problem, solved.
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Unit Vector Perpendicular to b, c at Angles cos⁻¹(-1/3) and π/3
Find alpha when a unit vector perpendicular to two given vectors also satisfies two angle conditions. A JEE Main 2025 3D vector problem, solved fully.
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3-Digit Numbers Divisible by 2 and 3, Not 4 and 9
How many 3-digit numbers are divisible by both 2 and 3, but not by 4 or 9? Solved using LCMs and arithmetic progressions, JEE Main 2025 style.
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The Length of the Chord of the Ellipse x²/4 + y²/2 = 1 Whose Mid-Point Is (1, 1/2) Is
Given only the midpoint of a chord of an ellipse, find its length using the T = S1 equation of a chord — a JEE Main 2025 conic sections problem, solved.