Calendar: 1893-1894 Page 841

FACULTY OF SCIENCE YEAR III 11 If tan2 3A tan2 12 tan tan2 Ζ 12 tan tan21 prove that one solution is given by sin 2A sin 18 12 Enunciate De Moivre's Theorem for any exponent and prove it for positive integer Write down the different values of cos and express in the simplest form of surds the roots of 13 Given that cos θ sin θ eto and cos θ sin θ ie expand cos θ in ascending powers of Θ Write down the sum of the infinite series cos 3a "cos 5a cos -- Η--- &c 14 Find the sum of the series sin β sin sin cos cos 2a cos 3a to infinity 15 Define the polar triangle and shew that if ar b'י cl be the sides of the polar triangle of ABC then a' π What triangle is its own polar triangle 16 If Β are the parts of spherical triangle quote equations such that when any three consecutive parts are given any one of the other parts may be determined without ambiguity 17 Establish the formulas tan If"" cot sin cos V'Sin sin sin and deduce the corresponding formula in Plane Trigono- metry