Trigonometry & Inverse Trigonometry
Grade 12
Question:
<p>Number of solutions of \(\tan^{-1}(2x)+\tan^{-1}(3x)=\pi/4\) for \(x\in(0,1)\):</p>
Step-by-Step Solution
<div class="solution"><p>Apply tan addition: $\frac{5x}{1-6x^2}=1\implies 6x^2+5x-1=0\implies x=1/6$ (in (0,1)) or $x=-1$ (rejected).</p><p><strong>Answer: 1 solution</strong></p><div class="key-concept"><strong>Key Concept:</strong> Sum of two tan⁻^1 = standard angle \to quadratic via addition formula
Correct Answer: 1