Let A, B=A−I, ω=(√3i−1)/2: Count n With Aⁿ+(ωB)ⁿ=A+B
Given A^n + (ωB)^n = A + B for ω a complex cube root of unity, how many n in 1..100 satisfy it? JEE Main 2022 matrix and complex numbers problem.
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If sin²10°sin20°sin40°sin50°sin70°=α−1/16sin10°, Find 16+1/α
A five-term trigonometric product from JEE Main 2022, reduced step by step using complementary angles and the sin a cos a identity.
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Position Vectors 4p+q-3r, -5p+q+2r, 2p-q+2r: Find α+2β+5γ
A JEE Main 2025 vector geometry problem solved using the Euler line property that the centroid divides the orthocenter-circumcenter segment 2:1.
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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.