Trigonometry & Inverse Trigonometry
Trigonometric Equations
Grade 11
Question:
<p>Find the number of solutions of the equations \(2\sin^2 x + \sin^2 2x = 2\) and \(\sin 2x + \cos 2x = \tan x\) in \([0, 4\pi]\) satisfying the condition \(2\cos 2x + \sin x \le 2\).</p>
Step-by-Step Solution
Key Concept: Find solutions common to both equations and filter by the inequality.
<p>This is the same as Exercise 6. Solve both equations simultaneously and apply the inequality constraint.</p>
Correct Answer: 8