# Calendar: 1899-1900 Page 766

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cxiv FACULTY OF SCIENCE 10 Establish formula connecting the cosine of the sum of two angles with the sines and cosines of the angles Prove that cos 3A cos 4A cos 5A sin 2A sin 2A sin Hence prove that cos 30 cos 40 cos 50 11 Prove that sin 3A sin sin 3A sin hA sin 20 sin 3A -f16 Hence prove that sin- sin and sin- sin 12 In any triangle prove that sin sin Β sin and that sin 2A sin 2Β or sin2 according as is acute or obtuse also that cos cos Β cos is positive 13 Solve the triangle for which 43786 38924 44 1816 14 On the sides of regular octagon sideitf equilateral triangles are described internally Find the area of the eight-rayed star formed by their other sides DREW MEDAL Sieometrg ant rtgonometrg If two triangles have two angles of the one equal to two angles of the other they shall be similar How many conditions must hold in order that two poly- gons of η sides may be similar Prove that two similar polygons may be so placed that lines joining corresponding vertices are concurrent Prove that three parallel planes cut any two straight lines proportionally If one corner of cube be joined to each of the other corners three tetrahedra are formed which are identically equal to one another straight line of given length slides between two fixed straight lines find the position in which the area of the triangle formed is maximum Show that in the hyperbola the locus of the foot of the perpendicular from the focus upon tangent is circle Construct conic given focus centre and tangent

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