Simplify cos(5x)cos(3x)

Problem

cos(5*x)*cos(3*x)

Solution

1. Identify the product-to-sum formula for the product of two cosines.

cos(A)*cos(B)=1/2*(cos(A−B)+cos(A+B))

2. Substitute the values A=5*x and B=3*x into the formula.

cos(5*x)*cos(3*x)=1/2*(cos(5*x−3*x)+cos(5*x+3*x))

3. Simplify the arguments inside the cosine functions by performing the subtraction and addition.

cos(5*x)*cos(3*x)=1/2*(cos(2*x)+cos(8*x))

Final Answer

cos(5*x)*cos(3*x)=1/2*(cos(2*x)+cos(8*x))

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