Question

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

Answer 1

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`