alleryStart learning →$\sin^2\theta + \cos^2\theta$ equals:
- $2$
- $0$
- $\tan\theta$
- $1$
Show answer and 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 $\sin^2\theta$: $\cot^2\theta + 1 = \csc^2\theta$.