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simplity. $\newline$ $\cos^3(x)+\sin^2(x)\cos(x)$

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Evaluate integers raised to rational exponents

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Q. simplity.

\newline

\cos^3(x)+\sin^2(x)\cos(x)

Recognize Identities: Recognize the trigonometric identities. $\newline$ We can use the Pythagorean identity $\sin^2(x) + \cos^2(x) = 1$ to simplify the expression.
Use Pythagorean Identity: Rewrite the expression using the Pythagorean identity. $\newline$ We can replace $\sin^2(x)$ with $1 - \cos^2(x)$ in the expression $\cos^3(x) + \sin^2(x) \cdot \cos(x)$ . $\newline$ $\cos^3(x) + (1 - \cos^2(x)) \cdot \cos(x)$
Rewrite Expression: Distribute the $\cos(x)$ in the second term. $\cos^3(x) + \cos(x) - \cos^3(x)$
Distribute $\cos(x)$ : Combine like terms. $\newline$ The terms $\cos^3(x)$ and $-\cos^3(x)$ cancel each other out, leaving us with: $\newline$ $\cos(x)$

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