Calendar: 1865-1866 Page 536

538 GENERAL LITERATURE AND SCIENCE Deduce from the former of the two preceding values sin 2a and sin 3a find also from the assumed value of cos -f- cos 2a and 3a and then find sine cosine and tangent of 36 If cos cos 4e sin 4a sin show that two values 21r jr of are and ץ The sides AB BC CA of triangle are in arithmetical progression and the difference of the squares of the shortest AB and of the common difference of the sides is to the square of BD which bisects in Β the side CA as also the sum of the squares of the sides is 116 Required the sides Prove that sin sin cos sin siu sin2 -- Prove that in triangle ABC IP 2ab cos deduce from this the tan If ABC be triangle and cos2 cos2 Β cos2 then one of the angles shall he right angle 10 AD and ΒΈ are perpendiculars from the angles and of the triangle ABC on the sides opposite show that DE cos 11 The radius of the circle inscribed in triangle ABC Β sin sin sec 12 Prove that whatever be the value of cos sin cos mA f- sin mA 18 13 If cos then A" 180 10 200 14 If two triangles have two sides of the one equal to two sides of the other each to each hut the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them of the other the base of that