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Answer from Sia

Posted about 2 months ago

Solution by Steps

step 1

We start by simplifying $\cos^3(x)$

step 2

Using the trigonometric identity, we have: $\cos^3(x) = \frac{1}{4} (3 \cos(x) + \cos(3x))$

step 3

Another way to express $\cos^3(x)$ is using the exponential form: $\cos^3(x) = \frac{1}{8} (e^{-ix} + e^{ix})^3$

Answer

$\cos^3(x) = \frac{1}{4} (3 \cos(x) + \cos(3x))$ or $\cos^3(x) = \frac{1}{8} (e^{-ix} + e^{ix})^3$

Key Concept

Simplification of $\cos^3(x)$ using trigonometric identities and exponential form

Explanation

The simplification of $\cos^3(x)$ can be achieved using trigonometric identities or by expressing it in terms of exponential functions. Both methods provide equivalent results.

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