Simplify 2cos(x/2)^2-1

Problem

2*cos2(x/2)−1

Solution

1. Identify the double-angle identity for cosine, which states cos(2*θ)=2*cos2(θ)−1

2. Substitute the value θ=x/2 into the identity.

3. Simplify the argument of the cosine function by calculating 2⋅x/2=x

Final Answer

2*cos2(x/2)−1=cos(x)

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