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Chisinau MO p50 1949-56 VIII-IX ctg(a/2)}> 1 + ctga for 0 <a < pi /2

Source:

March 15, 2021
trigonometryinequalitiesalgebra

Problem Statement

Prove the inequality: ctga2>1+ctgactg \frac{a}{2}> 1 + ctg a for 0<a<π20 <a <\frac{\pi}{2}