kittymeow8
kittymeow8 kittymeow8
  • 13-04-2017
  • Mathematics
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how to express cos 3x in terms of cosx

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LammettHash
LammettHash LammettHash
  • 13-04-2017
[tex]\cos3x=\cos(x+2x)=\cos x\cos2x-\sin x\sin2x[/tex]
[tex]=\cos x(\cos^2x-\sin^2x)-2\sin^2x\cos x[/tex]
[tex]=\cos^3x-\cos x\sin^2x-2\sin^2x\cos x[/tex]
[tex]=\cos^3x-3\cos x\sin^2x[/tex]
[tex]=\cos^3x-3\cos x(1-\cos^2x)[/tex]
[tex]=\cos^3x+3\cos^3x-3\cos x[/tex]
[tex]=4\cos^3x-3\cos x[/tex]
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