4-5 Cauchy Inequality in Senior High School Mathematics Elective Course
The two-dimensional form of Cauchy inequality (A 2+B 2) (C 2+D 2) ≥ (AC+BD) 2, so (A 2+B 2) (C 2+D 2) ≥ | AC+BD | Proof | A cosθ+B sinθ | 0? 5+b？ 0? 5)(cos？ 0? 5θ+sin？ 0? 5θ) = 1, that is |a cosθ+b sinθ|≤ 1.