Simplify 2cos(theta)^2-1

Problem

2*cos2(θ)−1

Solution

1. Identify the expression as a standard form used in trigonometric identities.

2. Recall the double angle identity for the cosine function, which states that cos(2*θ)=cos2(θ)−sin2(θ)

3. Substitute the Pythagorean identity sin2(θ)=1−cos2(θ) into the double angle formula.

4. Simplify the resulting expression: cos(2*θ)=cos2(θ)−(1−cos2(θ))=2*cos2(θ)−1

5. Conclude that the given expression is equivalent to the cosine of the double angle.

Final Answer

2*cos2(θ)−1=cos(2*θ)

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