Simplify cos(4x)cos(3x)+sin(4x)sin(3x)

Problem

cos(4*x)*cos(3*x)+sin(4*x)*sin(3*x)

Solution

1. Identify the trigonometric identity that matches the structure of the given expression.

2. Recall the cosine difference formula, which states that cos(A−B)=cos(A)*cos(B)+sin(A)*sin(B)

3. Assign the values from the expression to the variables in the formula, where A=4*x and B=3*x

4. Substitute these values into the condensed form of the identity.

cos(4*x−3*x)

5. Simplify the expression inside the parentheses by subtracting the terms.

4*x−3*x=x

Final Answer

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

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