Simplify 2cos(x)^2-1

Problem

2*cos^2(x)−1

Solution

1. Identify the expression as a standard form of a trigonometric identity.

2. Recall the double angle formula for the cosine function, which states that cos(2*x)=cos^2(x)−sin^2(x)

3. Substitute the Pythagorean identity sin^2(x)=1−cos^2(x) into the double angle formula to get cos(2*x)=cos^2(x)−(1−cos^2(x))

4. Simplify the resulting expression to see that cos(2*x)=2*cos^2(x)−1

Final Answer

2*cos^2(x)−1=cos(2*x)

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