Calendar: 1881-1882 Page 678

AND ENTRANCE EXHIBITIONS 679 16 Prove the identities tan2 45 tan2 45 cos nA cos j2 Λ cos2 sin2 17 Find tan Θ in terms of tan 2Θ and explain the ambiguity of sign Apply the formula to find tan 15c 18 In any triangle cos cos sin2 suftS sin2C cos cos Β cos £ ON tan- tan 19 How many sides and angles of triangle must be known if the triangle is to be solved What is the am- biguous case explain clearly by figures If the area of one of the triangles is times that of the other what restriction holds as to the comparative magnitude of the given sides 20 Given log 30103 and log 845098 find log2550 and solve for χ the equation 21 Prove De Moivre's Theorem for any index Obtain the six values of II £uclt& Hementaro onk£9 &c Two isosceles triangles cannot have common base unless the line joining their vertices or that line produced bisects the base at right angles Triangles upon equal bases and between the same parallels are equal to one another Divide parallelogram into four equal parts To describe square that shall be equal to given recti- lineal figure The apposite angles of any quadrilateral figure inscribed in circle are equal to two right angles If two adjacent angles of the quadrilateral so inscribed are equal two opposite sides will also be equal