allery$\sin^{2} 45^{\circ} + \cos^{2} 45^{\circ}$ equals:
A$0$
B$1$
C$\dfrac{1}{2}$
D$2$
Answer & Solution
Correct answer: B. $1$
Pythagorean identity: $\sin^{2}\theta + \cos^{2}\theta = 1$ for any $\theta$.
Direct check: $(1/\sqrt{2})^{2} + (1/\sqrt{2})^{2} = 1/2 + 1/2 = 1$ ✓.
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