Question

If \( \sin \theta + \cos \theta = 1 \), what is the value of \( \sin^2 \theta + \cos^2 \theta \)?

• A. 0
• B. 1
• C. 2
• D. -1

Hint:

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.

Answer 1

The Correct Option is B

We are given the equation \( \sin \theta + \cos \theta = 1 \). We need to find \( \sin^2 \theta + \cos^2 \theta \). Using the Pythagorean identity: \[ \sin^2 \theta + \cos^2 \theta = 1 \] This identity is always true for any angle \( \theta \), so regardless of the given equation, we know that: \[ \sin^2 \theta + \cos^2 \theta = 1. \] Thus, the value of \( \sin^2 \theta + \cos^2 \theta \) is \( 1 \).