Two 20 Newton forces act concurrently on an object what angle between these forces produce a resultant force with the greatest magnitude

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.