Calendar: 1885-1886 Page 675

general literature and science Solve the equations tan cot cos cos cos 40 Shew that in any triangle sin sin Js9 sin where is the area of the triangle and the circumradius person walks in straight line towards very distant object and observes that at points B9 the angles of elevation of the object are 2a 3a respectively Shew that AB BBC nearly The area of any triangle is to the area of the trnngle whose sides are respectively equal to the straight lines joining its angular points with the middle points of the opposite sides as Shew that sin cot 7r and solve sin sin Deduce from De Moivre's Theorem the expansion of sin in powers of Write down the corresponding ex- pansion for cos and verify as far as that sin 2x cos 2x 10 Express the cosine of one of the angles of right- angled spherical triangle in terms of the sides If be the right angle and CD bisects and CE is perpen- dicular to AB prove that cos cos tan tan -1- cos cos6 11 Shew how to solve triangle in which two angles and the side opposite one of them are given If the given side and the angle opposite to it be both obtuse consider whether the solution can be ambiguous 12 COD are two chords of circle at right angles