Calendar: 1876-1877 Page 586

586 GENERAL LITERATURE AND SCIENCE Prove geometrically that" cot cot cot ϋ cot -f- cot Solve the equation to cos 3θ sm-θ coe 20 and determine the limits of to that tliere may be two solutions between ο and 7r In plane triangle if α β γ be the perpendiculars from the angles on the opposite sides then py ay αβ when and It are tbe radii of the inscribed and circumscribed circles The length of the line drawn from the angle of triangle ABC bisecting Β and meeting the circumscribed circle is sin cosAs bl-Γ Expand β Vsin cos 10S10 sin Θ θ in ascending powers of as far as and hence shew that when β is small the method of proportional parts is not applicable to tables giving sin θ 10 g- Find an expression for the area of quadrilateral described in circle in the form If the product of the tangents of the angles of such quadri- lateral be unity shew that the sum of two of its angles will be three times that of the remaining two Prove De Moivre's theorem If be positive integer expand cos Θ 2" in series of cosines of multiples of Θ Sum the infinite series sinfl cos20 sin20 cos'0 sin3fl