Calendar: 1881-1882 Page 629

630 GENERAL LITERATURE AND SCIENCE τ יי 12 Define logarithm Explain what is meant by the base nx when מ is indefinitely increased is ex Hence deduce the exponential theorem and find series for log 13 Find the radius of circle inscribed in triangle If the centre of perpendiculars be joined to the angles of triangle and the radii of the circles inscribed in the three tri- angles so formed be rv r2 r3 then will r2 r3 -I- 422 14 Show that χϊη pn-1 x2 rcos Hence deduce the factors of sin Prove that 7r 2V2 £ £f and that 7r2 product of squares of the expressions on the right-hand side 15 Prove by induction that if χ -f cos then -f cos 710 xn Hence deduce De Moivre's Theorem for positive integers If ץ β ץ find χ and in terms of α β 16 Sum the following series 8in0cos0 -8in20cos20 r8 113 008 30 to מ terms λ sin30 sin 8in0 -1 sin20 η 2Δ η 0v -cosec sm cos-X- 1cot-