<p>The number of possible solutions of <em>x</em> such that <span>\(\sin^2 x + \cos^2 x = 1\)</span> is:</p>
Step-by-Step Solution
Key Concept: Recognize that sin²x + cos²x = 1 is a fundamental trigonometric identity that holds for ALL real values of x, not an equation to solve. The question asks for the count of solutions, which is infinite.
<p><strong>Step 1:</strong> Recognize that sin²x + cos²x = 1 is the fundamental Pythagorean trigonometric identity.</p><p><strong>Step 2:</strong> An identity is an equation that is true for ALL values of the variable in its domain. This identity holds for every real number x.</p><p><strong>Step 3:</strong> Since the equation is satisfied by every real value of x, the number of solutions is infinite.</p><p>∴ Answer: D (Infinite solutions)</p>
Correct Answer: D