Trigonometry & Inverse Trigonometry
Trigonometric Equations
Grade 11
Question:
<p>The number of solutions of the system of equations:<br/>\(2\sin^2 x + \sin^2 2x = 2\)<br/>\(\sin 2x + \cos 2x = \tan x\)<br/>in \([0, 4\pi]\) satisfying \(2\cos 2x + \sin x \le 2\) is:</p>
Step-by-Step Solution
Key Concept: Find the intersection of solution sets from multiple equations and then apply an inequality constraint.
<p>Solve each equation in the system separately, then find common solutions. Apply the additional constraint \(2\cos 2x + \sin x \le 2\) to filter solutions. Count those in \([0, 4\pi]\).</p>
Correct Answer: 8