Trigonometry & Inverse Trigonometry
Triangle Geometry
Grade 11
Question:
<p>In triangle ABC, a = 3, b = 4, c = 2. Point D and E trisect the side BC. If ∠DAE = θ, then cot 2θ is divisible by:</p>
<p>(a) 2</p>
<p>(b) 3</p>
<p>(c) 5</p>
<p>(d) 7</p>
Step-by-Step Solution
Key Concept: Use coordinate geometry with trisection points to find angles, then apply double angle formulas
<p>Let D and E trisect BC such that BD = DE = EC = 2/3 each. Using coordinate geometry and the angle formula, calculate ∠DAE and find cot 2θ.</p><p>The value cot 2θ is divisible by 3.</p>
Correct Answer: B