Cos alpha minus Cos beta=1 & cos alpha plus cos beta=1/e then ordered pair of alpha and beta is

We are given the equations:

cos(α) - cos(β) = 1
cos(α) + cos(β) = 1/e
Step 1: Adding the two equations
Adding both equations:

(cos(α) - cos(β)) + (cos(α) + cos(β)) = 1 + (1/e)

This simplifies to:

2cos(α) = 1 + (1/e)

Dividing both sides by 2:

cos(α) = (1 + 1/e)/2

Step 2: Subtracting the two equations
Subtracting the second equation from the first:

(cos(α) - cos(β)) - (cos(α) + cos(β)) = 1 - (1/e)

This simplifies to:

-2cos(β) = 1 - (1/e)

Dividing both sides by -2:

cos(β) = (1/e - 1)/2

Step 3: Finding the ordered pair (α, β)
Since α and β are angles, we take the inverse cosine to determine their values:

α = cos⁻¹[(1 + 1/e)/2]
β = cos⁻¹[(1/e - 1)/2]

Thus, the ordered pair (α, β) is:

( cos⁻¹[(1 + 1/e)/2], cos⁻¹[(1/e - 1)/2] )