Calendar: 1887-1888 Page 672

676 GENERAL LITERATURE AND SCIENCE 11 Prove that tan-H -f tan-1 £ tan-1 tan-1 ל3 and that cos cos--1 jt 12 The three sides of triangle are V6 and find the angles without the help of tables 13 Prove that sin sin sin HA Λ -- tan cos cos cos HA and that tan tan sin 14 Sum the series cos 2A cos sin sin β sin to מ terms -Conic Scrttoiuf Differential anK integral Calculus Prove that the equation 2f ry r2 3y represents two straight lines at right angles to each other the axes being rectangular The coordinates of Ρ are to and of φ are find the coordinates of point in such that μ ן si Mr1 ii1 PR RQ Prove that the lines 2x 3x f4 f5 all pass through one point Find the equation to the straight line which passes through the centres of the two circles a& 2χ -f and y2 2y Find the length of the common chord of the two circles 2ד far Determine the relations between the constants of the two equations Ix my δ and ra in order that the loci they represent may touch each other