Simplify 2cos(pi/12)^2-1

Problem

2*cos2(π/12)−1

Solution

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

2. Match the given expression to the identity by setting θ=π/12

3. Substitute the value of θ into the identity to rewrite the expression as cos(2⋅π/12)

4. Simplify the argument of the cosine function.

2⋅π/12=π/6

5. Evaluate the trigonometric function at the known angle.

cos(π/6)=√(,3)/2

Final Answer

2*cos2(π/12)−1=√(,3)/2

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