Trigonometry Examples

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

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \sin (x) + 1$ and $b = \sin (x) - 1$ .

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

Step 2

Simplify.

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Step 2.1

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

$(1 + 2 \sin (x) - 1) (\sin (x) + 1 - (\sin (x) - 1))$

Step 2.2

Subtract $1$ from $1$ .

$(0 + 2 \sin (x)) (\sin (x) + 1 - (\sin (x) - 1))$

Step 2.3

Add $0$ and $2 \sin (x)$ .

$2 \sin (x) (\sin (x) + 1 - (\sin (x) - 1))$

Step 2.4

Apply the distributive property.

$2 \sin (x) (\sin (x) + 1 - \sin (x) - - 1)$

Step 2.5

Multiply $- 1$ by $- 1$ .

$2 \sin (x) (\sin (x) + 1 - \sin (x) + 1)$

Step 2.6

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

$2 \sin (x) (0 + 1 + 1)$

Step 2.7

Add $0$ and $1$ .

$2 \sin (x) (1 + 1)$

Step 2.8

Add $1$ and $1$ .

$2 \sin (x) \cdot 2$

Step 2.9

Multiply $2$ by $2$ .

$4 \sin (x)$