Trigonometry & Inverse Trigonometry
Trigonometric Equations
Grade 11
Question:
<p>If the equation \(\cos 3x + \cos 2x = \sin \frac{x}{2} + \sin \frac{3x}{2}\) is satisfied for \(0 \leq x \leq 2\pi\), then the number of values of \(x\) is</p>
<p>(a) 6</p>
<p>(b) 7</p>
<p>(c) 4</p>
<p>(d) 5</p>
Step-by-Step Solution
Key Concept: Convert sum of cosines and sines to product form using sum-to-product formulas, then solve the resulting equation systematically.
<p>Solving the trigonometric equation $\cos 3x + \cos 2x = \sin \frac{x}{2} + \sin \frac{3x}{2}$ in the interval $[0, 2\pi]$ yields 7 distinct values of $x$.</p>
Correct Answer: b