Q2: The Power of Triangles

Geometry Level 5

Find the number of solutions to the equation: \[\cos ^n x - \sin ^n x = 1\] in the range \(0 \leq x < 2\pi\) , where \(n\) ranges through all positive integers.


This problem is part of the set IMO Training: Set 1. Please read the introductory note; this is not original!)
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