# Calendar: 1879-1880 Page 601

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GENERAL LITERATURE AND SCIENCE 601 Show that the limit when η is indefinitely increased of 3a cos- sin- is 3ע η η Explain the ambiguous case in the solution of triangles Shew that the nine point circles of the two triangles are equal If be the radius of the circle circumscribing the triangle ABC show that ן nT Β eiccos cos- cos Δ Δ Λ Show that the radius of the escribed circle opposite the angle of triangle is bcr be 4Rr' where Rr are the radii of the circumscribed and inscribed circles Prove Demoivre's Theorem Rationalize the expression sin sin β Sum the series sin2 2a sins3a Β1η ΊΓ cosa -f β f- 2cosa 43 cosa 3β to infinity 10 There are towers of known height and η feet and the angles of elevation are equal at points forming an equilateral triangle on the plane of the horizon show that the distance between the towers feet mn where ρ is side of the triangle 11 In any spherical triangle prove that cot sinC cote 8in4 cos cosi 12 ABC is spherical triangle each of whose sides is quadrant Ρ any point within the triangle prove that cosMP cos2RP cosaCP

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