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

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

Move $\sin^{2} (x)$ .

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

Rearrange terms.

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

Apply pythagorean identity.

$1 + \cos (x) - 1$

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

Subtract $1$ from $1$ .

$0 + \cos (x)$

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

$\cos (x)$