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

Problem

2*cos2(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*cos2(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*cos2(22.5)−1=√(,2)/2

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