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(sin x)^k + (cos x)^{-m} = (cos x)^k + (sin x)^{-m}

Source: Polish MO Recond Round 1990 p4

September 9, 2024

algebratrigonometry

Problem Statement

For each pair of even natural numbers

k

m

determine all real numbers

x

that satisfy the equation

(\sin x)^k + (\cos x)^{-m} = (\cos x)^k + (\sin x)^{-m}