Trigonometry Examples

$(c - s) (c + s) = c^{2} - s^{2}$

Step 1

Expand $(c - s) (c + s)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$c (c + s) - s (c + s) = c^{2} - s^{2}$

Step 1.2

Apply the distributive property.

$c \cdot c + c s - s (c + s) = c^{2} - s^{2}$

Step 1.3

Apply the distributive property.

$c \cdot c + c s - s c - s \cdot s = c^{2} - s^{2}$

Step 2

Combine the opposite terms in $c \cdot c + c s - s c - s \cdot s$ .

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Step 2.1

Reorder the factors in the terms $c s$ and $- s c$ .

$c \cdot c + c s - c s - s \cdot s = c^{2} - s^{2}$

Step 2.2

Subtract $c s$ from $c s$ .

$c \cdot c + 0 - s \cdot s = c^{2} - s^{2}$

Step 2.3

Add $c \cdot c$ and $0$ .

$c \cdot c - s \cdot s = c^{2} - s^{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $c$ by $c$ .

$c^{2} - s \cdot s = c^{2} - s^{2}$

Step 3.2

Multiply $s$ by $s$ by adding the exponents.

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Step 3.2.1

Move $s$ .

$c^{2} - (s \cdot s) = c^{2} - s^{2}$

Step 3.2.2

Multiply $s$ by $s$ .

$c^{2} - s^{2} = c^{2} - s^{2}$

Step 4

Since the two sides have been shown to be equivalent, the equation is an identity.

$(c - s) (c + s) = c^{2} - s^{2}$ is an identity.