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The sum of second derivatives of fractions k pi/4 (k odd)

Source: IMO LongList 1982 - P47

May 16, 2011
calculusderivativetrigonometryalgebra proposedalgebra

Problem Statement

Evaluate sec⁡′′π4+sec⁡′′3π4+sec⁡′′5π4+sec⁡′′7π4\sec'' \frac{\pi}4 +\sec'' \frac{3\pi}4+\sec'' \frac{5\pi}4+\sec'' \frac{7\pi}4. (Here sec⁡′′\sec'' means the second derivative of sec⁡\sec).
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