Simplify cos(2A)

Problem

cos(2*A)

Solution

1. Identify the expression as a double angle trigonometric identity for the cosine function.

2. Apply the formula for the double angle of cosine, which has three common equivalent forms based on the Pythagorean identity sin^2(A)+cos^2(A)=1

3. State the primary form derived from the sum formula cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B) where A=B

4. Derive alternative forms by substituting 1−sin^2(A) for cos^2(A) or 1−cos^2(A) for sin^2(A)

Final Answer

cos(2*A)=cos^2(A)−sin^2(A)=2*cos^2(A)−1=1−2*sin^2(A)

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