younaiskandar2005 younaiskandar2005

24-08-2022
Mathematics

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Use a counterexample to show cos(3x) = 3 cos x - 4 cos³ x is not an identity.

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LammettHash LammettHash

24-08-2022

Let [tex]x=\frac\pi3[/tex]. Then

[tex]\cos\left(\dfrac{3\pi}3\right) = \cos(\pi) = -1[/tex]

but

[tex]3\cos\left(\dfrac\pi3\right) - 4\cos^3\left(\dfrac\pi3\right) = \dfrac32 - \dfrac48 = 1[/tex]

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