Simplify be reducing to a single term :
`cos 5 theta cos 2 theta - sin 5 theta sin 2 theta.`

Answer

To simplify the expression \( \cos 5\theta \cos 2\theta - \sin 5\theta \sin 2\theta \), we can use the cosine addition formula. Here’s the step-by-step solution:

### Step 1: Write down the given expression
The given expression is:
\[ \cos 5\theta \cos 2\theta - \sin 5\theta \sin 2\theta \]

### Step 2: Identify the cosine addition formula
Recall the cosine addition formula:
\[ \cos(a + b) = \cos a \cos b - \sin a \sin b \]
In our case, we can identify \( a = 5\theta \) and \( b = 2\theta \).

### Step 3: Apply the cosine addition formula
Using the formula, we can rewrite the expression:
\[ \cos 5\theta \cos 2\theta - \sin 5\theta \sin 2\theta = \cos(5\theta + 2\theta) \]

### Step 4: Simplify the argument of the cosine
Now, simplify the argument:
\[ 5\theta + 2\theta = 7\theta \]

### Step 5: Write the final simplified expression
Thus, we have:
\[ \cos 5\theta \cos 2\theta - \sin 5\theta \sin 2\theta = \cos 7\theta \]

### Final Answer
The simplified expression is:
\[ \cos 7\theta \]

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