expression: sin²(π/10) + cos²(π/10).

Explanation:

Step1: Recall trigonometric identity

According to the Pythagorean - identity $\sin^{2}\theta+\cos^{2}\theta = 1$ for any real - number $\theta$.

Step2: Substitute $\theta=\frac{\pi}{10}$

Here $\theta=\frac{\pi}{10}$, so $\sin^{2}\left(\frac{\pi}{10}\right)+\cos^{2}\left(\frac{\pi}{10}\right)=1$.

Answer:

$1$