Answer:

Explanation:
We have been given the following trigonometric sum:

To express this sum as a product, we can use the cosine sum to product formula:

Rewrite the trigonometric sum as:

Apply the sum to product formula to the first two terms and the last two terms:



Factor out the common term 2cos(3x):
![2 \cos \left(3x\right)\left[\cos \left(10x\right) + \cos \left(4x\right) \right]](https://img.qammunity.org/2024/formulas/mathematics/high-school/ap6qt8kvrcl1rcba340zj7li8xn70n07mg.png)
Apply the sum to product formula again to the sum inside the parentheses, cos(10x) + cos(4x):
![2 \cos \left(3x\right)\left[2 \cos \left((10x+4x)/(2)\right) \cos \left((10x-4x)/(2)\right)\right]](https://img.qammunity.org/2024/formulas/mathematics/high-school/lr7xenhgp8i9rlh7d0h53jo8vpo9agpl69.png)
![2 \cos \left(3x\right)\left[2 \cos \left((14x)/(2)\right) \cos \left((6x)/(2)\right)\right]](https://img.qammunity.org/2024/formulas/mathematics/high-school/ppdoj4co066g0cas04vyb5mkn8k31uyd9r.png)
![2 \cos \left(3x\right)\left[2 \cos \left(7x\right) \cos \left(3x\right)\right]](https://img.qammunity.org/2024/formulas/mathematics/high-school/9fcrm6wyyf6petamfbndyhgjyb38540fnx.png)
Remove the unnecessary parentheses:

Multiply the numbers:

Rewrite cos(3x)cos(3x) as cos²(3x):

Therefore, the given trigonometric sum expressed as a product is:
