The exact value is cos(10- 80).
How to use addition and subtraction of angles formula
Given
cos10cos80 - sin10sin80
cos(10 - 80), we use the cosine difference formula:
cos(A - B) = cos Acos B + sin A sin B
In this case, A = 10 and B = 80
cos(10 - 80) = cos(10cos(80 + sin(10)sin(80)
Now substitute the values:
cos(10- 80) = cos(10)cos(80) + sin(10)sin(80)
= cos(10)cos(80) - sin(10)sin(80)
This simplifies to:
cos(10 - 80) = cos(10 - 80)
So, the exact value is cos(10- 80).