Question

The solution of the equation \[ \sin^2\theta + \cos^2\theta = 1 \] lies in the interval

• A. \( (-\pi/4, \pi/4) \)
• B. \( (-3\pi/4, 3\pi/4) \)
• C. \( (0, 2\pi) \)
• D. \( (-2\pi, 2\pi) \)

Hint:

The Pythagorean identity \( \sin^2\theta + \cos^2\theta = 1 \) holds for all values of \( \theta \) in the interval \( (0, 2\pi) \).

Answer 1

The Correct Option is C

This is a standard identity for trigonometric functions, and its solutions are valid for the interval \( (0, 2\pi) \).
Step 2: Conclusion.
The correct answer is (C), \( (0, 2\pi) \).