$\sin^2\theta + \cos^2\theta$ equals:
A$2$
B$0$
C$\tan\theta$
D$1$
Answer & Solution
Correct answer: D. $1$
The **Pythagorean identity** $\sin^2\theta + \cos^2\theta = 1$ holds for every real $\theta$. It comes from Pythagoras applied to the unit circle: any point on it has coordinates $(\cos\theta, \sin\theta)$ with distance 1 from origin, so the sum of squared coordinates is 1.
Companion identities:
- Dividing by $\cos^2\theta$: $1 + \tan^2\theta = \sec^2\theta$.
- Dividing by $\sin^2\theta$: $\cot^2\theta + 1 = \csc^2\theta$.
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