Calendar: 1869-1870 Page 510

512 GENERAL LITERATURE AND SCIENCE Prove that cos Β cos sin sin --- And that sin cos tan cot sec cosec δ Find Λ and from the equations sin Λ sin Β 3cos25 sin sin Β cos5 Prove that tan tan 3J tan 5A tan 5A tan 3A tan 2A From the top of tower the height of which is the depression of two points and on the ground in straight line passing through the base of the tower are and show that the distance between the points 2h tan 2a If Ot be the centre of escribed circle which touches Β and rl the radius and 02 of that which touches and r2 its radius then 02 r2 sec- The area of regular pentagon inscribed in circle area of pentagon described about it -f2 10 If two straight lines be parallel and one of them is at right angles to plane the other also shall be at right angles to the same plane 11 Every solid angle is contained by plane angles which together are less than four right angles 12 There are but five regular solids -Crigonomttry II Given the four sides of trapezoid parallel sides being ab the others cd find its area If Β 7r π Β π cos cos Β cos tan --- tan--- tan --- --- tail--- Lull --- -1------- cos cos -fcosC