Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number $\cos \left(5^{\circ}\right) \cos \left(85^{\circ}\right)-\sin \left(5^{\circ}\right) \sin \left(85^{\circ}\right)$ Find its exact value. Need Help?

Step 1 ：Given the expression \(\cos \left(5^{\circ}\right) \cos \left(85^{\circ}\right)-\sin \left(5^{\circ}\right) \sin \left(85^{\circ}\right)\)

Step 2 ：This expression is in the form of the cosine of the difference of two angles. The formula for the cosine of the difference of two angles is \(\cos(a - b) = \cos(a)\cos(b) + \sin(a)\sin(b)\)

Step 3 ：In this case, we have a subtraction instead of an addition in the formula, so we can rewrite the expression as the cosine of the difference of two angles. The two angles are 5 degrees and 85 degrees. So, the expression can be rewritten as \(\cos(5^{\circ} - 85^{\circ})\)

Step 4 ：The exact value of this expression can be found by calculating the cosine of the difference of the two angles.

Step 5 ：Final Answer: The exact value of the expression \(\cos \left(5^{\circ}\right) \cos \left(85^{\circ}\right)-\sin \left(5^{\circ}\right) \sin \left(85^{\circ}\right)\) is \(\boxed{0.17364817766693041}\)