Calendar: 1871-1872 Page 526

526 GENERAL LITERATURE AND SCIENCE 15 In right-angled triangle CD and CE are drawn from the right angle to the hypothenuse making angles and β with the hypothenuse of which β is the greater prove that the area of the triangle CDEit cot cot 16 Show how to find the area of regular polygon of η sides circumscribing circle of given radius Deduce the expression for the area of circle 17 Three equal circles touch each other externally find the space included between them Find the same when the circles are unequal and their radii as the numbers 18 If cosec θ sin θ and sec θ cos θ prove that ab ai bi 19 Prove that tan-1 tan-1 tan-1 tan-1 3τ 5T 84 And solve tan-1 -tan-1 Ζ 20 Prove that in any triangle Ιβη 2Λ '- itan And find the angles when 3c 7b and 3724 having given log 30103 tan 188762408 42 tan 149-1604569 tan 139-1603083 "50 21 If in the three edges which meet at one angle of cube three points be taken at distances from the angle respectively the area of the triangle ABC formed by joining the three points is equal to £ α2έ2 aV lr