The question is solve [tex]2 + cos2x=3cosx[/tex] for 0<- X <-2pi greater/equal to zero and less than or equal to 2pi.(adsbygoogle = window.adsbygoogle || []).push({});

My solution

[tex]2+cos2x=3cosx[/tex]

[tex]2+cosx^2-sin^2=3cosx[/tex]

[tex]2+cosx^2-(1-cosx^2)=3cosx[/tex]

[tex]2+2cosx^2-1-3cosx=0[/tex]

[tex]2cos^2-3cosx+1=0[/tex]

Factoring

[tex]2x^2-3x+1=0[/tex]

[tex](2x-1)(x-1)=0[/tex]

[tex]x=1 or x=1/2[/tex]

solving for cos i get

[tex]cos(x)=1 --> x=0[/tex]

[tex]cos(x)=1/2 -->x= pi/3 or 5pi/3[/tex]

Did i do this Right?

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# Homework Help: Solve 2+cos2x=3cosx

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