Calendar: 1872-1873 Page 536
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GENERAL LITERATURE AND SCIENCE 537 points an angle equal to the semi-difference of the other two angles 16 Find the area of regular polygon of η sides described about circle of radius and deduce the expression for the area of the circle The area of regular polygon inscribed in circle is mean proportional between the areas of an inscribed and circum- scribed regular polygon of half the number of sides 17 If the tangents of the angles of triangle be as the num- bers find them and show that if be the sides of the triangle ana plptp3 the perpendiculars on the sides from the opposite angles then 5p1p2p3 3abc 18 Is the triangle right-angled or not if sin2 sin2i sin2c 19 The straight line which bisects the vertical angle of triangle divides the base into two parts which are to each other as to Having given find tan and adapt the result for logarithmic computation both when is greater and less than 20 Prove De Moivre's formula for any index Obtain the six values of VII -aigtbra anil Crigononutri Simplify the expression ab "י י Prove that ax1 bx has the same sign for all real values of except such as lie between two real values which render the expression equal to zero Eliminate χ andy from ax xy and solve the equations 2xf 2- xy- y1
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