8th VMO 1969 Problem A2 Find all real x such that 0 < x < π and 8/(3 sin x - sin 3x) + 3 sin 2 x ≤ 5.
π/2 Solution We have 3 sin x - sin 3x = 4 sin 3 x. Put s = sin x. Then we want 2/s 3 + 3s 2 ≤ 5. Note that since 0  5 with equality iff s = 1, so we must have sin x = 1 and hence x = π/2. Thanks to Suat Namli 8th VMO 1969 © John Scholes jscholes@kalva.demon.co.uk 7 March 2004 Last corrected/updated 7 Mar 04