Calendar: 1882-1883 Page 635

632 GENERAL LITERATURE AND SCIENCE Give geometrical proofs for the expansions of sine 04 sine tan Prove that Kine sine sine1 sine2Z and hence show that sine2 sine2i 42 sin -4 -י Β sin Β cos sin2 10 Prove that in any triangle Β cos cosi cos sin sin -sin י Δ ץ sin sin Β smC c2 cos ---י 2ab and prove a2 £2 cot δ2 cot c2 a2 cot Β 11 man walking along straight road observes the directions with respect to the road of two objects when the angle which they subtend is greatest and then measures the distance from the point of observation to the point whence they appear in the same straight line find the distance between them 12 If and be respectively the radii of the circles in- scribed in and described about triangle prove that Β מ sin sin cos 2sim4 and show that acotA -f bcotB ccotC 13 Prove that 2Χ7Γ θ -T π 4- θ cos-'- ν sin-'- η η when λ has any integral value admits of η different values and no more Express the eighth roots of unity