Simplify 1/2(-sin(x)^2-cos(x)^2)

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

Step 1

Simplify with factoring out.

Factor $- 1$ out of $- \sin^{2} (x)$ .

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

Factor $- 1$ out of $- \cos^{2} (x)$ .

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

Factor $- 1$ out of $- (\sin^{2} (x)) - (\cos^{2} (x))$ .

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

Step 2

Apply pythagorean identity.

$\frac{1}{2} \cdot (- 1 \cdot 1)$

Step 3

Combine fractions.

Multiply $- 1$ by $1$ .

$\frac{1}{2} \cdot - 1$

Combine $\frac{1}{2}$ and $- 1$ .

$\frac{- 1}{2}$

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$