Precalculus Examples

$\cos (x) (1 - \cos (x))$

Step 1

Apply the distributive property.

$\cos (x) \cdot 1 + \cos (x) (- \cos (x))$

Step 2

Simplify the expression.

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Step 2.1

Multiply $\cos (x)$ by $1$ .

$\cos (x) + \cos (x) (- \cos (x))$

Step 2.2

Rewrite using the commutative property of multiplication.

$\cos (x) - \cos (x) \cos (x)$

Step 3

Multiply $- \cos (x) \cos (x)$ .

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Step 3.1

Raise $\cos (x)$ to the power of $1$ .

$\cos (x) - (\cos^{1} (x) \cos (x))$

Step 3.2

Raise $\cos (x)$ to the power of $1$ .

$\cos (x) - (\cos^{1} (x) \cos^{1} (x))$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\cos (x) - {\cos (x)}^{1 + 1}$

Step 3.4

Add $1$ and $1$ .

$\cos (x) - \cos^{2} (x)$