SOLUTION: Write the sum as a product: cos(14.3a) + cos(7.1a)

All you need are the formulas for 

cos(A+B) = cos(A)cos(B)-sin(A)sin(B)
cos(A-B) = cos(A)cos(B)+sin(A)sin(B)

If you add these equations, the second terms will cancel.

So what you do is let A be the average of the two angles.
The average angle is the exact same amount more than the 
smaller angle as it is less than the larger angle.  So
we let B be that common difference. 

The average of 14.3a and 7.1a is 10.7a, which is 3.9a more 
than 7.1a and 3.9a less than the l4.3a.

So let A = 10.7a and B = 3.9a

Then 

cos(14.3a) = cos(10.7a+3.9a) = cos(10.7a)cos(3.9a)-sin(10.7a)sin(3.9a)
 cos(7.1a) = cos(10.7a-3.9a) = cos(10.7a)cos(3.9a)+sin(10.7a)sin(3.9a)

Adding the two equations above gives:

cos(14.3a) + cos(7.1a) = 2cos(10.7a)cos(3.9a)

That's all you need do.  No need for another formula to memorize.

Edwin