Trigonometry & Inverse Trigonometry
Trigonometric Equations
Grade 11
Question:
<p>The equation \(2\cos^2\frac{x}{2} - \sin^2 x = x^2 + x - 2\), where \(x < \frac{9}{2}\), has</p>
<p>(a) no real solution</p>
<p>(b) one real solution</p>
<p>(c) more than one real solutions</p>
<p>(d) None of the above</p>
Step-by-Step Solution
Key Concept: Compare the ranges of trigonometric and polynomial functions to determine the number of solutions.
<p>This is Question 116. Analyze by considering the range of the left side (trigonometric) and right side (quadratic) to determine the number of intersection points.</p>
Correct Answer: B