MathDB

5

Part of 1971 Swedish Mathematical Competition

Problems(1)

max |1 - a \cos x| >= \tan^2 (t/2) when |x|<= t, a>0, 0<t< \pi/2

Source: 1971 Swedish Mathematical Competition p5

3/26/2021
Show that max⁡∣x∣≤t∣1−acos⁡x∣≥tan⁡2t2 \max\limits_{|x|\leq t} |1 - a \cos x| \geq \tan^2 \frac{t}{2} for aa positive and t∈(0,π2)t \in (0, \frac{\pi}{2}).
algebratrigonometryinequalitiesmax