# Calendar: 1899-1900 Page 820

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entrance exhibitions II -Cvigononutn anti ftrttymtttt Warneford and SambrooJce Candidates omit questions 1-5 Define the secant of an angle Prove that sec cos cannot He between and Find if sec cos Prove geometrically or otherwise that cosec 2A -f cot 2A cot Hence deduce the sum of η terms of the series cosec 2A cosec 4A cosec There are two mountains heights 2000 ft and 3000 ft treating them as right-angled cones with their axes 2000 ft apart find the height of the pass between them and the distance from the top of one down to the pass and up to the top of the other If are the radii of the circumcircle and incircle of triangle the distance between their centres prove that -2Rr If the triangle be right-angled express in terms of the sides and verify the above formula Express cos ηθ in terms of powers of cos Θ Under what circumstances can sin 710 be expressed in terms of powers of sin θ If square number ends in prove that the preceding figure is odd 6£ Simplify ן and give the justification of each step Prove that 256623 and 192278 have the same as 85541 and 96139 Express 15625 and 16384 as vulgar fractions in their lowest terms also ffff and as decimal fractions 10 Prove that decimal fraction that neither terminates nor recurs cannot be expressed as vulgar fraction How do such decimal fractions arise 11 Find the sum and difference and if you can the product and quotient of of £4 3s Id and 035 of £247 18s 4d

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