Question

Find the exact value of cos(x - y) if cos(x) = 3/5 and cos(y) = 4/5.

Answer 1

The exact value of cos(x - y) can be found using the cosine difference formula and the given values of cos(x) and cos(y).

Step-by-step explanation:

To find the exact value of cos(x - y), we can use the cosine difference formula which states that cos(x - y) = cos(x)cos(y) + sin(x)sin(y). Given that cos(x) = 3/5 and cos(y) = 4/5, we can substitute these values into the formula to get: cos(x - y) = (3/5)(4/5) + sqrt(1 - (3/5)^2)sqrt(1 - (4/5)^2). Simplifying further gives us the exact value of cos(x - y).