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