Simplify 2cos(x/2)^2

Problem

2*cos(x/2)

Solution

1. Identify the power-reduction identity for the cosine function.

2*cos(θ)=1+cos(2*θ)

2. Substitute the given angle x/2 for θ into the identity.

θ=x/2

3. Apply the formula by multiplying the angle by 2

2*(x/2)=x

4. Simplify the expression using the result of the substitution.

1+cos(x)

Final Answer

2*cos(x/2)=1+cos(x)

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