Algebra Examples

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

Step 1

Start on the left side.

$(1 - \sin (x)) (1 + \sin (x))$

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Apply the distributive property.

$1 (1 + \sin (x)) - \sin (x) (1 + \sin (x))$

Step 2.1.2

Apply the distributive property.

$1 \cdot 1 + 1 \sin (x) - \sin (x) (1 + \sin (x))$

Step 2.1.3

Apply the distributive property.

$1 \cdot 1 + 1 \sin (x) - \sin (x) \cdot 1 - \sin (x) \sin (x)$

Step 2.2

Simplify and combine like terms.

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

Step 3

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

$(1 - \sin (x)) (1 + \sin (x)) = 1 - \sin^{2} (x)$ is an identity