Simplify cos(2u)

Problem

cos(2*u)

Solution

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

2. Apply the identity for the cosine of a double angle, which has three common forms.

3. Select the primary form derived from the sum of angles formula: cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B)

4. Substitute A=u and B=u to get cos(2*u)=cos2(u)−sin2(u)

5. Alternative forms can be derived using the Pythagorean identity sin2(u)+cos2(u)=1 resulting in 2*cos2(u)−1 or 1−2*sin2(u)

Final Answer

cos(2*u)=cos2(u)−sin2(u)

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