Trigonometry & Inverse Trigonometry
Trigonometric Inequalities
Grade 11
Question:
<p>The complete set of values of \(x\) satisfying \(\frac{2\sin 6x}{\sin x - 1} < 0\) and \(\sec^2 x - 2\sqrt{2}\tan x \le 0\) in \(\left(0, \frac{\pi}{2}\right)\) is \([a, b) \cup (c, d]\). Find the value of \(\frac{cd}{ab}\).</p>
Step-by-Step Solution
Key Concept: Combine conditions from rational and quadratic inequalities, then identify the union of disjoint intervals.
<p>Analyze each inequality separately: First, determine where the rational expression is negative by examining numerator and denominator signs. Second, solve the quadratic in \(\tan x\) to find the range satisfying the second inequality. Find the intersection in the given interval.</p>
Correct Answer: 6