Trigonometry Examples

$(2 - 2 \sin (x)) (2 + 2 \sin (x))$

Step 1

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

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Step 1.1

Apply the distributive property.

$2 (2 + 2 \sin (x)) - 2 \sin (x) (2 + 2 \sin (x))$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $2 \cdot 2 + 2 (2 \sin (x)) - 2 \sin (x) \cdot 2 - 2 \sin (x) (2 \sin (x))$ .

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Step 2.1.1

Reorder the factors in the terms $2 (2 \sin (x))$ and $- 2 \sin (x) \cdot 2$ .

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

Step 2.1.2

Subtract $2 \cdot 2 \sin (x)$ from $2 \cdot 2 \sin (x)$ .

$2 \cdot 2 + 0 - 2 \sin (x) (2 \sin (x))$

Step 2.1.3

Add $2 \cdot 2$ and $0$ .

$2 \cdot 2 - 2 \sin (x) (2 \sin (x))$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $2$ by $2$ .

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

Step 2.2.2

Multiply $- 2 \sin (x) (2 \sin (x))$ .

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Step 2.2.2.1

Multiply $2$ by $- 2$ .

$4 - 4 \sin (x) \sin (x)$

Step 2.2.2.2

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

$4 - 4 (\sin^{1} (x) \sin (x))$

Step 2.2.2.3

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

$4 - 4 (\sin^{1} (x) \sin^{1} (x))$

Step 2.2.2.4

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

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

Step 2.2.2.5

Add $1$ and $1$ .

$4 - 4 \sin^{2} (x)$

Step 2.3

Simplify with factoring out.

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Step 2.3.1

Factor $4$ out of $4$ .

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

Step 2.3.2

Factor $4$ out of $- 4 \sin^{2} (x)$ .

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

Step 2.3.3

Factor $4$ out of $4 (1) + 4 (- \sin^{2} (x))$ .

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

Step 3

Apply pythagorean identity.

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