Trigonometry Examples

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

Step 1

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

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

Step 2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 \sin (x) = 2 \cdot 1 \cdot \sin (x)$

Step 3

Rewrite the polynomial.

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

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 1$ and $b = \sin (x)$ .

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