IMO 1967 LL ROM42

Decompose into real factors the expression 1 −sin5 x−cos5 x.

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IMO 1967 LL ROM42

Origin: ROM

Problem

Decompose into real factors the expression 1 −sin5 x−cos5 x.

Solution

E = (1−sin x)(1−cos x)[3+2(sin x+cos x)+2 sin x cos x+sin x cos x(sin x+ cos x)].