Trigonometry Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify each term.

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Step 2.1

Multiply $1$ by $1$ .

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

Step 2.2

Multiply $- \sin (x)$ by $1$ .

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

Step 2.3

Multiply $\cos (x)$ by $1$ .

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

Step 2.4

Rewrite using the commutative property of multiplication.

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