Calendar: 1874-1875 Page 548

548 GENERAL LITERATURE AND SCIENCE 14 Prove that chord radius χ sin AB AC are chords of arcs of 60 and 90 in circle whose centre is if AB OC be produced to meet in the arc whose chord DC has its cosine and chord equal 15 Determine θ in the equations 2sin0 tan cos30 co820 cos0 sina -f sin sin 20 sin 4- -f sin 20 16 Determine the limits between which must lie that we may have 2cos sin sin 17 If cos cosjB cos Β then tan tan tan are in harmonical progression If Β be three angles whose cosines are in harmonical progression then cos Fcos 18 If be an integer of the form im or im -f- then ן מ nrt η tiB nC smnA sinaif sm C7 4sm cos cos-cos- τ 19 Sin0 ΒΪηφ sin φ can only be true equation when one of the quantities β φ and θ φ or multiple of 360 20 In any triangle the length of perpendicular from 011 £'sini e2sin2 the opposite side -- -- 21 The area of triangle 2abc ABC ac sini --- cos cos cos 22 Solve the equation 1252 given 60 log 4771213 cot 9"49 10 7618797 difference for 10007014 find the other angles