Calendar: 1869-1870 Page 511

GENERAL LITERATURE AND SCIENCE 513 If tan-1 χ sin-1 show that χ sin 18 Prove that tan-1 £ tan-1 The chord of the segment of circle is equal to the radius show that the circle is divided into two areas which are as 107r -f 3V3" 2π -3V3 If he the sides of the triangle ABC andp be perpendiculars on them from the opposite angles then ρ"1 ψ be ac ab qr pr י" fq Τ2 י" c2 י If the tangents of the semi-angles of triangle are in Arithmetical Progression prove that the sides are also in Arith- metical Progression An equilateral triangle square and hexagon have equal areas find their perimeters and show that that of the hexagon is least Find cos 15 and apply the result to find the roots of ir3 V2 10 Assuming that cos η X" -- show that xn cos cos ךA- -7 cos 5A 21 cos 3A 35 cos 11 If θ be small so that the powers above CP may be neg- lected and if sin θ Αθ B63 find in terms of from the equation sin 2Θ sin θ cos θ find also 12 If sin χ -- sin 2x -f- sin Sx &c to infinity sin χ tan -f cos Φ XI -Conic tton$ Investigate the equation to straight line in terms of the perpendicular from the origin and its inclination to the axis of Κ Κ