IMO 1969 LL GDR29

Find all real numbers \lambda such that the equation

imolonglistmathematicsolympiad

IMO 1969 LL GDR29

Origin: GDR

Problem

Find all real numbers \lambda such that the equation sin4 x −cos4 x = \lambda(tan4 x −cot4 x) (a) has no solution, (b) has exactly one solution, (c) has exactly two solutions, (d) has more than two solutions (in the interval (0, \pi/4)).