Problem: Find the least positive integer nnn such that
1sin45∘sin46∘+1sin47∘sin48∘+⋯+1sin133∘sin134∘=1sinn∘.\frac 1{\sin 45^\circ\sin 46^\circ}+\frac 1{\sin 47^\circ\sin 48^\circ}+\cdots+\frac 1{\sin 133^\circ\sin 134^\circ}=\frac 1{\sin n^\circ}. sin45∘sin46∘1+sin47∘sin48∘1+⋯+sin133∘sin134∘1=sinn∘1.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions