The value of `(sin5alpha-sin3alpha)/(cos5alpha+2cos4alpha+cos3alpha)` is

Explanation

To solve the expression \((\sin 5\alpha - \sin 3\alpha) / (\cos 5\alpha + 2\cos 4\alpha + \cos 3\alpha)\), we can follow these steps:

### Step 1: Apply the sine difference formula
We know that the formula for the difference of sines is:
\[ \sin c - \sin d = 2 \cos\left(\frac{c + d}{2}\right) \sin\left(\frac{c - d}{2}\right) \]
Here, let \(c = 5\alpha\) and \(d = 3\alpha\). Therefore:
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