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  Item Reference: KCLCAL-1876-1877-587

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GENERAL LITERATURE AND SCIENCE 587 10 Find an expression for the distance between tbe centre of the inscribed circle of triangle and tbe 01 thocentre and shew that the distance between the centres of the inscribed and nine point circles is equal to the difference of their radii 11 In spherical triangle prove the formula cosa cos cos -f- sin sin cos If cosa cosi -f- cose cos b- -c -f cos cos then cosec -f- cosec cosec cot cot cot 12 If the sides of spherical triangle be in arithmetical progression prove that sin sin cos-- sin3 13 Arcs are drawn from the angular points of spherical triangle to the middle points of the opposite sides prove that they intersect in point which divides each arc into portions of which the sines have to each other the ratio of twice the conine of the bisected side to unity XVIII -JDtffmnttal anfc ntcg ral Calculus Find the differential coefficients of xr tan ax log and Prove the equation hi hf ΘΚ θ being proper fraction and finite and continuous between the limits χ and χ Hence prove that 12 י tan tan1 Shew that '- -- if η be positive
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