Calendar: 1877-1878 Page 591

general literature and science 589 Apply it to the equation x7 3x 11 Prove Sturm's theorem and by means of it determine the number of real roots in the above equation 12 Give Cordan's solution of cubic and apply it to tbe equation x3 5x XVIII plant anti &pijtriral Crigononutrj Prove that β Β Β Β zcos- cos- COS- 8111 sin '- sin τ Solve the equations eos0 sin sin sing Prove that the limit of cmfl yan2 ן VV2 2sin0 when θ is ft are the vertices of equilateral triangles described on the same base BC any other point prove that AD2 Αΰ a2 e2 where α έ are the sides of ABC If ζ be the sides of the squares inscribed in the triangle ABC or the sides then will i- 1- χ ζ ο τ being the radius of the inscribed circle If -f- 7r show that tan-1 tan tan tan-l tan tan- tan-i tan tan