Simplify cos(4x)+cos(2x)

Problem

cos(4*x)+cos(2*x)

Solution

1. Identify the sum-to-product identity for cosine, which states cos(A)+cos(B)=2*cos((A+B)/2)*cos((A−B)/2)

2. Assign the variables A=4*x and B=2*x

3. Substitute these values into the identity:

2*cos((4*x+2*x)/2)*cos((4*x−2*x)/2)

4. Simplify the arguments inside the cosine functions:

2*cos((6*x)/2)*cos((2*x)/2)

5. Reduce the fractions to find the final simplified form:

2*cos(3*x)*cos(x)

Final Answer

cos(4*x)+cos(2*x)=2*cos(3*x)*cos(x)

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