Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $- 1$ by $1$ .

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

Step 1.3

Multiply $- - \sin (x)$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.3.2

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

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

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $1 + \sin (x) - 1 + \sin (x)$ .

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Step 2.1.1

Subtract $1$ from $1$ .

$0 + \sin (x) + \sin (x)$

Step 2.1.2

Add $0$ and $\sin (x)$ .

$\sin (x) + \sin (x)$

Step 2.2

Add $\sin (x)$ and $\sin (x)$ .

$2 \sin (x)$