Calculus Examples

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

Step 1

Rewrite ${(2 - \cos (x))}^{2}$ as $(2 - \cos (x)) (2 - \cos (x))$ .

$(2 - \cos (x)) (2 - \cos (x))$

Step 2

Expand $(2 - \cos (x)) (2 - \cos (x))$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 (2 - \cos (x)) - \cos (x) (2 - \cos (x))$

Step 2.2

Apply the distributive property.

$2 \cdot 2 + 2 (- \cos (x)) - \cos (x) (2 - \cos (x))$

Step 2.3

Apply the distributive property.

$2 \cdot 2 + 2 (- \cos (x)) - \cos (x) \cdot 2 - \cos (x) (- \cos (x))$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $2$ .

$4 + 2 (- \cos (x)) - \cos (x) \cdot 2 - \cos (x) (- \cos (x))$

Step 3.1.2

Multiply $- 1$ by $2$ .

$4 - 2 \cos (x) - \cos (x) \cdot 2 - \cos (x) (- \cos (x))$

Step 3.1.3

Multiply $2$ by $- 1$ .

$4 - 2 \cos (x) - 2 \cos (x) - \cos (x) (- \cos (x))$

Step 3.1.4

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

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

$4 - 2 \cos (x) - 2 \cos (x) + 1 \cos (x) \cos (x)$

Step 3.1.4.2

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

$4 - 2 \cos (x) - 2 \cos (x) + \cos (x) \cos (x)$

Step 3.1.4.3

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

$4 - 2 \cos (x) - 2 \cos (x) + \cos^{1} (x) \cos (x)$

Step 3.1.4.4

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

$4 - 2 \cos (x) - 2 \cos (x) + \cos^{1} (x) \cos^{1} (x)$

Step 3.1.4.5

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

$4 - 2 \cos (x) - 2 \cos (x) + {\cos (x)}^{1 + 1}$

Step 3.1.4.6

Add $1$ and $1$ .

$4 - 2 \cos (x) - 2 \cos (x) + \cos^{2} (x)$

Step 3.2

Subtract $2 \cos (x)$ from $- 2 \cos (x)$ .

$4 - 4 \cos (x) + \cos^{2} (x)$