Expand the Trigonometric Expression cos(2x)

Problem

cos(2*x)

Solution

1. Identify the double angle identity 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 A=x and B=x into the sum formula to get cos(x+x)=cos(x)*cos(x)−sin(x)*sin(x)

4. Simplify the expression by combining the trigonometric terms into squares.

Final Answer

cos(2*x)=cos2(x)−sin2(x)

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