If \( \sin \theta + \cos \theta = 1 \), what is the value of \( \sin^2 \theta + \cos^2 \theta \)?
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The identity \( \sin^2 \theta + \cos^2 \theta = 1 \) holds true for all angles. This is fundamental to trigonometry and is useful when simplifying expressions involving trigonometric functions.
The Pythagorean identity states that \( \sin^2 \theta + \cos^2 \theta = 1 \) for any angle \( \theta \). Therefore, regardless of the provided equation \( \sin \theta + \cos \theta = 1 \), the value of \( \sin^2 \theta + \cos^2 \theta \) is definitively \( 1 \).