Questions: Express the given sum or difference as a product of sines and/or cosines. cos(3θ/2) - cos(5θ/2)

Express the given sum or difference as a product of sines and/or cosines. cos(3θ/2) - cos(5θ/2)
Transcript text: Express the given sum or difference as a product of sines and/or cosines. \[ \cos \frac{3 \theta}{2}-\cos \frac{5 \theta}{2} \]
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Solution

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Solution Steps

Step 1: Identify the Type of Expression and Applicable Identity

Given the expression type as 'difference' and function types as ['cosine', 'cosine'], we use the identity: $\cos A - \cos B = -2 \sin\left(\frac{A + B}{2}\right) \sin\left(\frac{A - B}{2}\right)$.

Step 2: Apply the Identity to the Given Expression

Substituting \(A = 1.5x\) and \(B = 2.5x\) into the identity, we get: $$ -2 * sin((1.5x + 2.5x) / 2) * sin((1.5x - 2.5x) / 2) $$

Final Answer:

The transformed expression is: $$ -2 * sin((1.5x + 2.5x) / 2) * sin((1.5x - 2.5x) / 2) $$ rounded to 0 decimal places if necessary.

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