<p>∫₋π/₃^0 cot⁻¹(cot 2cos x − 1/(2cos x − 1))dx is equal to</p>
Step-by-Step Solution
Key Concept: Using trigonometric identities to simplify inverse trigonometric expressions before integration.
<p><strong>Step 1:</strong> Simplify the inverse cotangent expression using trigonometric identities.</p><p><strong>Step 2:</strong> The argument of cot⁻¹ simplifies to a standard form.</p><p><strong>Step 3:</strong> Integrate the simplified expression over [−π/3, 0].</p><p><strong>Step 4:</strong> The result is 2/3.</p><p>∴ Answer is (A).</p>
Correct Answer: A