Saurabh Koranglekar
Last Activity: 5 Years ago
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] )