Calendar: 1877-1878 Page 588

586 GENERAL LITERATURE AND SCIENCE term of זג Prove also that י ν χ η fx aV 2a 11 '' -1rL- 13 The number of degrees in one of the acute angles of right- angled triangle is to the number of grades in the otherjas to 20 determine the angles 14 Find all the values of where η is any integer 15 Give geometrical proofs for the expansions of s'11 -j- and cotan 16 Solve the equations sin β cosfl -r V2 cos cos70 CO340 tani cotan sin tan θ tan 17 Prove tanA tan2 4tan4 8cotan8 cotan sin Ζ An 4sin3 and shew that if triangle be such that it is possible to draw straight line AD meeting Cin 80 that the angle BAD is one-third of the angle BAG and also BD one-third of BC then β C- 8c 18 Prove that in any triangle tan tani tanC tan tanB tanC and thence deduce that if the perpendiculars drawn from the angles of triangle on the opposite sides meet in BC AC ΛΒ BC AC AB OA OB 00 OA OB 00 19 Prove that in any triangle cosB -f- cos cosA f- cosi cosC sini AnC a3 2a4 cos 60 c2 24ccos 60