Let θ₁ and θ₂ be the angles between the two forces and the direction of motion.
To produce motion in the indicated direction, the net force is
F = 20 cos θ₁ + 20 cos θ₂
= 20 (cos θ₁ + cos θ₂)
= 40 cos [(θ₁+θ₂)/2] cos[(θ₁-θ₂)/2]
The maximum value of the cosine function is 1, and it occurs when its argument is zero.
Therefore the maximum value of F occurs when
θ₁ + θ₂ = 0
or
θ₁ - θ₂ = 0
Add the two equations to obtain
2 θ₁ = 0 => θ₁ = 0
Also, θ₂ = θ₁ = 0
Answer: The angle between the two forces is zero.
