Question

express the given product as a sum or difference containing only sines or cosines. cos(3x)cos(5x)

Explanation:

Step1: Use the product - to - sum formula

The formula for \(\cos A\cos B=\frac{1}{2}[\cos(A + B)+\cos(A - B)]\). Here \(A = 3x\) and \(B=5x\).

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Step2: Simplify the expressions inside the cosine functions

Simplify \(3x + 5x=8x\) and \(3x-5x=-2x\). Since \(\cos(-\theta)=\cos\theta\), we have:

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Answer:

\(\frac{1}{2}\cos(8x)+\frac{1}{2}\cos(2x)\)