Simplify

Problem

cos(223.5*x)*cos(−15.5*x)−sin(223.5*x)*sin(−15.5*x)

Solution

1. Identify the trigonometric identity that matches the structure of the expression. The expression follows the form cos(A)*cos(B)−sin(A)*sin(B)

2. Apply the formula for the cosine of a sum, which states cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B)

3. Substitute the values A=223.5*x and B=−15.5*x into the sum formula.

cos(223.5*x+(−15.5*x))

4. Simplify the expression inside the parentheses by performing the subtraction.

223.5*x−15.5*x=208*x

Final Answer

cos(223.5*x)*cos(−15.5*x)−sin(223.5*x)*sin(−15.5*x)=cos(208*x)

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