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

asked Jun 22, 2023 35.5k views

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Let
$x=\frac\pi3$ . Then

$\cos\left(\frac{3\pi}3\right) = \cos(\pi) = -1$

but

$3\cos\left(\frac\pi3\right) - 4\cos^3\left(\frac\pi3\right) = \frac32 - \frac48 = 1$

Minillinim answered Jun 27, 2023

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