Trigonometry Examples

$(3 - 3 \sin (x)) (3 + 3 \sin (x))$

Step 1

Expand $(3 - 3 \sin (x)) (3 + 3 \sin (x))$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 (3 + 3 \sin (x)) - 3 \sin (x) (3 + 3 \sin (x))$

Step 1.2

Apply the distributive property.

$3 \cdot 3 + 3 (3 \sin (x)) - 3 \sin (x) (3 + 3 \sin (x))$

Step 1.3

Apply the distributive property.

$3 \cdot 3 + 3 (3 \sin (x)) - 3 \sin (x) \cdot 3 - 3 \sin (x) (3 \sin (x))$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $3 \cdot 3 + 3 (3 \sin (x)) - 3 \sin (x) \cdot 3 - 3 \sin (x) (3 \sin (x))$ .

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Step 2.1.1

Reorder the factors in the terms $3 (3 \sin (x))$ and $- 3 \sin (x) \cdot 3$ .

$3 \cdot 3 + 3 \cdot 3 \sin (x) - 3 \cdot 3 \sin (x) - 3 \sin (x) (3 \sin (x))$

Step 2.1.2

Subtract $3 \cdot 3 \sin (x)$ from $3 \cdot 3 \sin (x)$ .

$3 \cdot 3 + 0 - 3 \sin (x) (3 \sin (x))$

Step 2.1.3

Add $3 \cdot 3$ and $0$ .

$3 \cdot 3 - 3 \sin (x) (3 \sin (x))$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $3$ by $3$ .

$9 - 3 \sin (x) (3 \sin (x))$

Step 2.2.2

Multiply $- 3 \sin (x) (3 \sin (x))$ .

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Step 2.2.2.1

Multiply $3$ by $- 3$ .

$9 - 9 \sin (x) \sin (x)$

Step 2.2.2.2

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

$9 - 9 (\sin^{1} (x) \sin (x))$

Step 2.2.2.3

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

$9 - 9 (\sin^{1} (x) \sin^{1} (x))$

Step 2.2.2.4

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

$9 - 9 {\sin (x)}^{1 + 1}$

Step 2.2.2.5

Add $1$ and $1$ .

$9 - 9 \sin^{2} (x)$

Step 2.3

Simplify with factoring out.

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Step 2.3.1

Factor $9$ out of $9$ .

$9 (1) - 9 \sin^{2} (x)$

Step 2.3.2

Factor $9$ out of $- 9 \sin^{2} (x)$ .

$9 (1) + 9 (- \sin^{2} (x))$

Step 2.3.3

Factor $9$ out of $9 (1) + 9 (- \sin^{2} (x))$ .

$9 (1 - \sin^{2} (x))$

Step 3

Apply pythagorean identity.

$9 \cos^{2} (x)$