trigonometric identities

Question

The identity sin²θ + cos²θ equals

RankGuru · Accepted Answer

1. **Definition**: In the unit circle, for any angle $	heta$, the coordinates are $(x, y) = (\cos 	heta, \sin 	heta)$.
2. **Unit Circle Equation**: The equation of the unit circle is $x^2 + y^2 = 1$.
3. **Substitution**: Replacing $x$ and $y$ gives **$\cos^2 	heta + \sin^2 	heta = 1$**.
4. **Conclusion**: This is the fundamental identity valid for all real and complex values of $	heta$.

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