Convert complementary angles

Using the identity $\sin \theta = \cos(90° - \theta)$, rewrite $\sin^2 27°$ as $\cos^2(90° - 27°) = \cos^2 63°$. Similarly, $\cos^2 73° = \sin^2(90° - 73°) = \sin^2 17°$.

$\sin^2 27° = \cos^2 63°, \cos^2 73° = \sin^2 17°$

Group terms and apply identity

Substitute the converted values: $(\sin^2 63° + \cos^2 63°) + (\cos^2 17° + \sin^2 17°) + \cos^2 90°$. Applying $\sin^2 \theta + \cos^2 \theta = 1$ to each pair.

$1 + 1 + \cos^2 90°$

Evaluate remaining term

We know $\cos 90° = 0$, so $\cos^2 90° = 0^2 = 0$. The final expression is $1 + 1 + 0 = 2$. However, reviewing the original expression: $\sin^2 63 + \cos^2 63$ (from $27$) = 1, $\cos^2 17 + \sin^2 17$ (from $73$) = 1. Total = 2.

$1 + 1 + 0 = 2$