Calendar: 1898-1899 Page 781

ENTRANCE EXHIBITIONS CxllX Prove geometrically that tan tan tan 2A If tan express tan 3A If are any angles express sin sin Β sin as sum of sines and if are the angles of triangle express sin il sm sin ל as product of cosines If are the perpendiculars from the vertices of triangle on the opposite sides the bisectors of the angles prove that pqrf fgh 00 cos £ C- cos £ With point on the circumference of circle as centre an arc is described to bisect the area of the circle If φ be the angle which the arc subtends at the point prove that sin φ φ cos φ ΐ7τ In dividing by 693 obtain quotient consisting of figures and remainder 528 my second remainder was 94 but it should have beenl94 what correction must apply to the result Prove that the of 23992091 and 8209897 is the of 6376 and 7572297 Write out table of square measure using only the following units square inch-square foot-square yard- square chain-square furlong-square mile How many angels are there in an army of angels occupy- ing cubic furlong if each angel occupies cube the edge of which is 20 feet Determine without fully performing the operations the order of the highest di it and what that digit is in the result of 03756 389648-5-Ό008471 10 Calculate 87 per cent of the value of 27 obligations of 500 francs at 2517 francs to the £ 11 Find the number of cubic inches there would be in 10 lbs of water if in rainfall of Ό1 inch ton of water falls on an acre 12 An increase of Id in the £ in the rate of tax causes diminution of per cent in the amount to be taxed the tax being raised from 66 to Id the extra receipts are £31 000 what was the amount taxed