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Putnam 1957 A3

Source: Putnam 1957

July 1, 2022
Putnamtrigonometryinequalitiescosine

Problem Statement

Let a,ba,b be real numbers and kk a positive integer. Show that ∣cos⁡kbcos⁡a−cos⁡kacos⁡bcos⁡b−cos⁡a∣<k2−1 \left| \frac{ \cos kb \cos a - \cos ka \cos b}{\cos b -\cos a} \right|<k^2 -1 whenever the left side is defined.
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