Equilibrium of Two Uniform Rods over a Cylinder: Solution

[Idiot_1]

Homework Statement

Two equal uniform rods AB & AC of weight W & length 2a are jointed smoothly at A. Two rods are kept freely under equilibrium over a smooth circular cylinder of radius r where axis of cylinder to be horizontal. If both rods inclined at an angle ɵ to the horizontal. Show that a cos³ɵ.cosecɵ = r

Homework Equations

Sin rule
$$\frac{A}{SinA}$$=$$\frac{B}{SinB}$$ = $$\frac{C}{SinC}$$
Cosine rule
a² = b² + c² + 2bc cosA

The Attempt at a Solution

Applying cosine rule

r² = r² + 4a² + 4ra cos(90-ɵ)
4a² = 4ra sinɵ
a = r sinɵ
r = a cosecɵ

i got this answer, help me to reach above answer

 

[member 553083]

.a cos3ɵ.cosecɵ = a3 sinɵ cosɵ cosecɵ = a3 sin2ɵ = r2a2 cos 3ɵ.cosecɵ = r2r = a cos3ɵ.cosecɵ