Calendar: 1870-1871 Page 517

GENERAL LITERATURE AND SCIENCE 517 If θ be the circular measure of an angle sin θ β θ β -f cob cos -3 cos 53 Hence prove that when is small sin θ Ρ Eliminate θ between tbe equations χ cos θ -J- cos Θ sin β sin β Investigate an expression for the cosine of the angle of triangle in terms of the sides Tbe sides of given triangle are and the angles α β prove that if point be taken within an equilateral triangle whose distances from its angles are proportional to the angles between these distances will be ft צי Expand 10ga -x in series of ascending powers of Prove that sin2 χ sin log sec χ sin χ -1- Τ &c 10 In any triangle cos cos Β cos 2C cos cos Β cos 41 -f c2 tan e2 i2 tan Jr Perimeter cos β- ϊ c"s c4 cos 11 Find the values of sin 165 sin 69 sin 11 15 π 27r 31r Show that cos cos יד cos 12 An observer at point wishing to discover the din- tance of an object on horizontal plane walks distance η directly towards to point then back to and along straight road to point such that AD AB he finds the