Expand the Trigonometric Expression cos(2A)

Problem

cos(2*A)

Solution

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

2. Apply the formula for the cosine of a sum, where cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B)

3. Substitute B=A into the sum formula to get cos(A+A)=cos(A)*cos(A)−sin(A)*sin(A)

4. Simplify the terms by writing them as squares.

Final Answer

cos(2*A)=cos2(A)−sin2(A)

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