 Hi and welcome to our session. In this class, the following question, the question says three forces P, Q and R acting on a point are in equilibrium. If the angle between force P and force Q would double the angle between force R and force P proved that PQ is equal to Q squared minus R squared. Let's now begin with the solution, let alpha be the angle between force P and force R. Angle between P and Q would double the angle between R and P. That means if angle between force P and force Q is to alpha, then we have to prove that PQ is equal to Q squared minus R squared. So now we have this angle as 2 alpha. This angle will be equal to 360 minus 3 alpha. We are given that all these three forces are in equilibrium. So since three forces are in equilibrium, P alpha is equal to Q by sine alpha is equal to P by minus sine 3 alpha to Q by sine. This is equal to Q squared. We can write sine minus cos squared to Q squared. We have 1 minus 4 cos squared.