Calendar: 1873-1874 Page 541

GENERAL LITERATURE AND SCIENCE 541 sin -ζ---- Vl tan cos cot cos cot cos cot cos sin sin Λ cos £ cos sin Β Prove sin Λ tan cos cot sec cosec vers 180 vers £ 180 vers 180 tan' tan tan if tau20 cos cos 3r cos cos cos χ cos Prove that יד ו λ Β Β cos -f cos iJ cos -1- cos ד And express coswi cos מ θ cosrfl by the sum of series of cosines of multiples of Θ Prove that tan tan β tan γ tan tan β tan sin -f- β cos cos β cosy when α β γ are any angles Modify this result when α β γ are the angles of triangle Solve the equations sin θ cos V3 sin θ cos θ V2 sin θ sin θ sin sin Find from the equation tan3 θ tan θ β and show that it will not be real unless sin he less than