Calendar: 1877-1878 Page 592

590 GENERAL LITERATURE AND SCIENCE sin sin -sin "ί ta1 siu2a sin2 sin2yj Prove Demoivre's theorem Find the real part of β φ Resolve into factors and prove that 27r 3π 7r -l cos cos cos---- cos -- 211 211 If r2 r3 be the radii of the inscribed and escribed circles of triangle shew that r2 r3 3r Λ Β atan-- ע tan--1- ctan 10 If Ο be tbe centre of the nine-point circle of ABC prove that Λ02 Λ2 2ל a2 where ii is the radius of t' ie circumscribed circle 11 Prove that tbe sines of tbe sides of spherical triangle are proportional to the sines of tbe opposite angles If p1 be the lengths of arcs drawn com perpendicular to an arc which meets AA1 at an angle shew that sin2 sin2 -f- 2sinjo npl cosAA1 sin2a 8111s A1 12 If in spherical triangle AP bisect the angle mee ng BC in Ρ and AQ be drawn perpendicular to tbe side BC prove that η ר sins sinfi ian PQ 2tan -ל- ----£ sine sin Deduce the corresponding formula in lane trigonometry 13 If the bisectors of the angles Β of spherical triangle are at right angles sin sing tan tan