Find All Complex Solutions cos(theta)^2+sin(theta)^2=1

$\cos^{2} (θ) + \sin^{2} (θ) = 1$

Subtract $1$ from both sides of the equation.

$\cos^{2} (θ) + \sin^{2} (θ) - 1 = 0$

Simplify $\cos^{2} (θ) + \sin^{2} (θ) - 1$ .

Rearrange terms.

$\sin^{2} (θ) + \cos^{2} (θ) - 1 = 0$

Apply pythagorean identity.

$1 - 1 = 0$

Subtract $1$ from $1$ .

$0 = 0$

Since $0 = 0$ , the equation will always be true.

Always true