Find the Exact Value 2cos(22.5)^2-1

Problem

2*cos^2(22.5^∘)−1

Solution

1. Identify the expression as a specific form of a trigonometric identity.

2. Recall the double-angle identity for the cosine function, which states cos(2*θ)=2*cos^2(θ)−1

3. Substitute θ=22.5^∘ into the identity to simplify the expression.

4. Calculate the resulting angle: 2×22.5^∘=45^∘

5. Evaluate the exact value of cos(45^∘) using the unit circle or special triangles.

Final Answer

2*cos^2(22.5^∘)−1=√(,2)/2

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