Identify the Identity

Recognize that the expression follows the standard trigonometric identity $\sin^2(\theta) + \cos^2(\theta) = 1$ for any value of $\theta$.

$\sin^2(\theta) + \cos^2(\theta) = 1$

Apply Identity

Since the angle in the expression $\sin^2(30°) + \cos^2(30°)$ is $\theta = 30°$ for both terms, the sum must be 1.

$\sin^2(30°) + \cos^2(30°) = 1$

Verification

Calculating manually: $\sin(30°) = 1/2$ and $\cos(30°) = \sqrt{3}/2$. Squaring them gives $(1/2)^2 + (\sqrt{3}/2)^2 = 1/4 + 3/4 = 4/4 = 1$.

$\left(\frac{1}{2}\right)^2 + \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{1}{4} + \frac{3}{4} = 1$