Lami’s theorem

Lami’s theorem

Lami's Theorem is related to the magnitudes of concurrent, coplanar, and non-collinear forces that maintain an object in static equilibrium. Lami's Theorem states that When three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two forces.
Let us consider three forces, A, B and C, acting on a particle or rigid body, making angles α, β and γ with each other.

Mathematically it can be expressed as-

Lami's theorem states that if the three coplanar concurrent forces acting on a body keep it in equilibrium, then

A. Each force is proportional to the cosine of the angle between the other two forces.
B. Each force is proportional to the cotangent of the angle between the other two forces.
C. Each force is proportional to the tangent of the angle between the other two forces.
D. Each force is proportional to the sine of the angle between the other two forces.

Answer

Option D is correct answer.
Each force is proportional to the sine of the angle between the other two forces. See statement of the Lami's Theorem.