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A3

Part of 1957 Putnam

Problems(1)

Putnam 1957 A3

Source: Putnam 1957

7/1/2022
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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