Calendar: 1878-1879 Page 595

GENERAL LITERATURE AND SCIENCE Find the sum of the series to terms 10 Express as continued fraction and Rai the first four convergent 11 Explain Cardan's method of solving cubic equation and apply it to x3 12x- 12 12 Enunciate and prove Sturm's theorem 13 Define determinant and prove that if two rows or two 01 umns be identical the determinant vanishes XXII Plan anU pijmcal Cvtsonomttvu If tan 45 tan2 Β then secA tan JsecA tan 2cosec25 Prove geometrically that C09A cosi 2cos-'-- cos-- τ In triangle the diameter of the circumscribing circle cos cos Β co 2sin sin if sin Shew how to solve triangle when the sides and the angle are given If there be two triangles having the given parts and if Cj c2 be the third sides the distance between the centres of the circuin- scribing circles is 2mA Find the values of θ which satisfy the equation sin20 sec40 cosf cos2A Prove that tan cosec2 cot sec2 cosec2 sec2 4cosec4 Ρ Ρ