Trigonometry Examples

$4 \sin^{2} (x) - 1$

Step 1

Rewrite $4 \sin^{2} (x)$ as ${(2 \sin (x))}^{2}$ .

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

Step 2

Rewrite $1$ as $1^{2}$ .

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

Step 3

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

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