Calendar: 1871-1872 Page 525

GENERAL LITERATURE AND SCIENCE 525 Solve the equations sin2 θ cos Θ tan2 θ tan θ sin6 θ cos6 and being acute angles prove that sin sin cos cos sin cos ί cos cos Β sin sin Deduce expressions for sin cos and tan in terms of Find also the greatest value of sin cos Show geometrically that sin 2A 2sin Prove that cos cos cos -j- cos and deduce that cos cos cos2 η sin2 10 If 180 prove that sin sin Β cos cos cos Hence deduce that sin2 sin2 Β sin2 cos cos Β cos 11 At the foot of mountain the elevation of its summit is 45 after ascending one mile up slope of 30 its elevation is found to be 60 Required the height of the mountain 12 Define the term logarithm and show that the logarithm of product is equal to tbe sum of the logarithms of its factors Write down the characteristics of log 27 to the base and of log 004 to base Solve 125 241 given log 30103 13 Prove that in any triangle cos -ב -- lab cos cos Show that in triangle right-angled at 14 The sides of triangle are three consecutive numbers and the greatest angle is double the least determine the triangle