Calendar: 1878-1879 Page 601

GENERAL LITERATURE AND SCIENCE 599 18 Prove tan tan 2tan2d sin0 tan0 cos cotfl sec0 cosectf 19 Shew that in any triangle sin sin cos cosB cosO and deduce the following sin2 Λ sin2£ sin2 2cos cos£ cosO cosi cos£7-j- cos cosA cosC cosi cos cosi cosC 20 Given tan2a cos cos$ cosa tun3 cosa cusu cos shew that tan tan2i tan2 21 What is the ambiguous case in the solution of triangle Explain by figure Shew that if the area of one of the triangles i- times that of the other the ratio of the greater to the less of the t'iven sides is less than 22 The elevation of tower is observed At station feet ntarer the elevation is the complement of the former feet nearer still it is double the first elevation Required the height of the tower 23 Ο is the centre of the circle circumscribing triangle and AO is produced to meet BC in shew that DO cos AO cosA 24 Three circles radii rx r2 r3 touch each other externally prove that the tangents at the point of contact meet in point whose distance from any one of them is 25 Prove that the area of circle of radius is equal to 7n If denote the area of the circle inscribed in triangle al a2 n3 the areas of the escribed circles then