<p>If cos 2θ = (√2 + 1) cos θ - 1/√2, then the value of θ is</p>
Step-by-Step Solution
Key Concept: Convert cos 2θ to 2cos²θ - 1 and solve the resulting quadratic equation in cos θ.
<p><strong>Step 1:</strong> Given cos 2θ = (√2 + 1) cos θ - 1/√2</p><p><strong>Step 2:</strong> Using cos 2θ = 2cos²θ - 1, we have 2cos²θ - 1 = (√2 + 1) cos θ - 1/√2</p><p><strong>Step 3:</strong> Rearranging: 2cos²θ - (√2 + 1) cos θ - 1 + 1/√2 = 0</p><p><strong>Step 4:</strong> This simplifies to 2cos²θ - (√2 + 1) cos θ + (√2 - 1)/√2 = 0</p><p><strong>Step 5:</strong> Solving gives cos θ = 1/√2, so θ = 2nπ ± π/4</p><p>∴ Answer is (b).</p>
Correct Answer: b