Trigonometry Examples

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

Step 1

Rewrite ${(\cos (x) + 1)}^{2}$ as $(\cos (x) + 1) (\cos (x) + 1)$ .

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

Step 2

Expand $(\cos (x) + 1) (\cos (x) + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $\cos (x) \cos (x)$ .

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Step 3.1.1.1

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

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

Step 3.1.1.2

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

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

Step 3.1.1.3

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

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

Step 3.1.1.4

Add $1$ and $1$ .

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Multiply $1$ by $1$ .

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

Step 3.2

Add $\cos (x)$ and $\cos (x)$ .

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