Simplify 2cos(15)^2-1

Problem

2*cos^2(15^∘)−1

Solution

1. Identify the expression as a form of the double-angle identity for cosine.

2. Recall the trigonometric identity cos(2*θ)=2*cos^2(θ)−1

3. Substitute θ=15^∘ into the identity to rewrite the expression.

2*cos^2(15^∘)−1=cos(2⋅15^∘)

4. Simplify the argument of the cosine function.

cos(2⋅15^∘)=cos(30^∘)

5. Evaluate the cosine of 30^∘ using the unit circle or standard trigonometric values.

cos(30^∘)=√(,3)/2

Final Answer

2*cos^2(15^∘)−1=√(,3)/2

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