Trigonometry Examples

$(5 - 5 \sin (x)) (5 + 5 \sin (x))$

Step 1

Expand $(5 - 5 \sin (x)) (5 + 5 \sin (x))$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 (5 + 5 \sin (x)) - 5 \sin (x) (5 + 5 \sin (x))$

Step 1.2

Apply the distributive property.

$5 \cdot 5 + 5 (5 \sin (x)) - 5 \sin (x) (5 + 5 \sin (x))$

Step 1.3

Apply the distributive property.

$5 \cdot 5 + 5 (5 \sin (x)) - 5 \sin (x) \cdot 5 - 5 \sin (x) (5 \sin (x))$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $5 \cdot 5 + 5 (5 \sin (x)) - 5 \sin (x) \cdot 5 - 5 \sin (x) (5 \sin (x))$ .

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Step 2.1.1

Reorder the factors in the terms $5 (5 \sin (x))$ and $- 5 \sin (x) \cdot 5$ .

$5 \cdot 5 + 5 \cdot 5 \sin (x) - 5 \cdot 5 \sin (x) - 5 \sin (x) (5 \sin (x))$

Step 2.1.2

Subtract $5 \cdot 5 \sin (x)$ from $5 \cdot 5 \sin (x)$ .

$5 \cdot 5 + 0 - 5 \sin (x) (5 \sin (x))$

Step 2.1.3

Add $5 \cdot 5$ and $0$ .

$5 \cdot 5 - 5 \sin (x) (5 \sin (x))$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $5$ by $5$ .

$25 - 5 \sin (x) (5 \sin (x))$

Step 2.2.2

Multiply $- 5 \sin (x) (5 \sin (x))$ .

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Step 2.2.2.1

Multiply $5$ by $- 5$ .

$25 - 25 \sin (x) \sin (x)$

Step 2.2.2.2

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

$25 - 25 (\sin^{1} (x) \sin (x))$

Step 2.2.2.3

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

$25 - 25 (\sin^{1} (x) \sin^{1} (x))$

Step 2.2.2.4

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

$25 - 25 {\sin (x)}^{1 + 1}$

Step 2.2.2.5

Add $1$ and $1$ .

$25 - 25 \sin^{2} (x)$

Step 2.3

Simplify with factoring out.

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Step 2.3.1

Factor $25$ out of $25$ .

$25 (1) - 25 \sin^{2} (x)$

Step 2.3.2

Factor $25$ out of $- 25 \sin^{2} (x)$ .

$25 (1) + 25 (- \sin^{2} (x))$

Step 2.3.3

Factor $25$ out of $25 (1) + 25 (- \sin^{2} (x))$ .

$25 (1 - \sin^{2} (x))$

Step 3

Apply pythagorean identity.

$25 \cos^{2} (x)$