<p>If cot θ + cot(π/4 - θ) = 2, then the general value of θ is</p>
Step-by-Step Solution
Key Concept: Expand cot(π/4 - θ) using the cotangent difference formula and solve the resulting trigonometric equation.
<p><strong>Step 1:</strong> We have cot θ + cot(π/4 - θ) = 2</p><p><strong>Step 2:</strong> Using cot A + cot B formula or expanding cot(π/4 - θ) = (cot π/4 · cot θ + 1)/(cot θ - cot π/4) = (cot θ + 1)/(cot θ - 1)</p><p><strong>Step 3:</strong> Setting up: cot θ + (cot θ + 1)/(cot θ - 1) = 2</p><p><strong>Step 4:</strong> Simplifying: cot²θ - cot θ + cot θ + 1 = 2(cot θ - 1), which gives cot²θ = 2cot θ - 3, or cot²θ - 2cot θ + 3 = 0</p><p><strong>Step 5:</strong> Solving: cot θ = √3, so θ = nπ ± π/6 (rechecking shows θ = nπ ± π/3)</p><p>∴ Answer is (c).</p>
Correct Answer: c