Simplify cos(2x)^2

Problem

cos2(2*x)

Solution

1. Identify the expression as the square of the cosine function with an argument of 2*x

2. Apply the power-reduction formula for cosine, which states cos2(θ)=(1+cos(2*θ))/2

3. Substitute the argument θ=2*x into the formula.

4. Simplify the resulting argument by multiplying 2⋅2*x=4*x

5. Distribute the fraction to write the expression in its simplest linear form.

Final Answer

cos2(2*x)=1/2+cos(4*x)/2

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