# Calendar: 1899-1900 Page 767

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FACULTY OF SCIENCE CXV Prove that cos cos cos Β sin sin when are less than one right angle ii when Β are each less than two' right angles but greater than one right angle Show that if cos-i cos-1 then cos sin2a a2 b2 ab In any triangle prove that cosO ccosB a2 2cos2- £ sin2 cot θ cot η cot where is the inclination to PC of line drawn from cutting BC in ratio Prove that if δ is the distance between the centres of the inscribed and circumscribed circles of any triangle δ2 R2 2Rr If two circles are concentric and if polygon be inscribed to one and circumscribed to the other show that there is one ratio of the radii for which this is possible for triangle or quadrilateral but two for pentagon or hexagon and draw the figures Prove that cosfta sin η is one of the values of cos sin By means of the identity show that β Ί η γ α ί00 γ ο sin--ί-sm 2α sm '- sm λβ -- sin sin 2γ sin -ZJ sin 8in £ sill β Snm to terms the series sin sin β sin

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