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Question Number 120882 by shaker last updated on 03/Nov/20

Answered by $@y@m last updated on 03/Nov/20

cos^3 x+cos x=1−cos^2 x cos x(cos^2 x+1)=sin^2 x cos x(2−sin^2 x)=sin^2 x cos^2 x(2−sin^2 x)^2 =sin^4 x (1−sin^2 x)(4+sin^4 x−4sin^2 x)=sin^4 x 4+sin^4 x−4sin^2 x−4sin^2 x−sin^6 x+4sin^4 x=sin^4 x sin^6 x−4sin^4 x+8sin^2 x−4=0 sin^6 x−4sin^4 x+8sin^2 x+3=7

cos3x+cosx=1−cos2xcosx(cos2x+1)=sin2xcosx(2−sin2x)=sin2xcos2x(2−sin2x)2=sin4x(1−sin2x)(4+sin4x−4sin2x)=sin4x4+sin4x−4sin2x−4sin2x−sin6x+4sin4x=sin4xsin6x−4sin4x+8sin2x−4=0sin6x−4sin4x+8sin2x+3=7

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