[tex]\bf cos(3x)\implies cos(2x+x)\\\\
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\underline{cos(2x)} cos(x)-\underline{sin(2x)} sin(x)
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\underline{[1-2sin^2(x)]} cos(x)-\underline{[2sin(x)cos(x)]} sin(x)
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cos(x)-2sin^2(x)cos(x)-2sin^2(x)cos(x)
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cos(x)-4sin^2(x)cos(x)\\\\
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\boxed{cos(3x) \ne cos^2(x)-3sin^2(x)cos(x)}[/tex]
