Trigonometry & Inverse Trigonometry
Trigonometric Equations
Grade 11
Question:
<p>If <span style='font-family: Arial'>sin A / sin B = 5/2</span> and <span style='font-family: Arial'>cos A / cos B = 3/2</span>, where <span style='font-family: Arial'>0 < A, B < π/2</span>, then</p>
<p>(a) <span style='font-family: Arial'>tan A = 3/5</span></p>
<p>(b) <span style='font-family: Arial'>tan A = 5/3</span></p>
<p>(c) <span style='font-family: Arial'>tan A = 2</span></p>
<p>(d) <span style='font-family: Arial'>tan B = 2</span></p>
Step-by-Step Solution
Key Concept: Divide the given sine ratio by the cosine ratio to find the tangent ratio.
<p><strong>Step 1:</strong> From the given conditions: <span style='font-family: Arial'>sin A / sin B = 5/2</span> and <span style='font-family: Arial'>cos A / cos B = 3/2</span></p><p><strong>Step 2:</strong> Dividing: <span style='font-family: Arial'>tan A / tan B = (5/2) / (3/2) = 5/3</span></p><p><strong>Step 3:</strong> Using <span style='font-family: Arial'>sin² A + cos² A = 1</span>, we can verify <span style='font-family: Arial'>tan A = 5/3</span></p><p>∴ Answer is B.</p>
Correct Answer: B