Calendar: 1885-1886 Page 680

672 GENERAL LITERATURE AND SCIENCE Express the sine and cosine of the sum of two angles in terms of the sines and the cosines of the angles themselves Hence deduce 8m'2A 2smA cos cos2A cos2A sin 2A 3sin sin 3A sin cos 2A Prove that tan HA an tan2 tan tan 60 tan 120 tan ZA sin sin 33 sin 39 sin 42 sin 51 sin 57 Solve the equations tan cos cos cos 40 If 180 prove that sin2J sin 25 sin2C sin sin sin tan tan jB tan tan tan tan cos cos jB -f cos sin sin sin and shew that the expression cot -will retain sin sin the same value if any two of the quantities be inter- changed Shew that in any triangle 2R sin smi sinC cibc where is the area of the triangle and the radius 2aS of the circumscribing circle Shew how to solve triangle when two sides are given and the included angle Two sides are 80 and 100 feet and the included angle is 60 10g3 47712 tanl0 53'36" 928432 person walks in straight line towards very distant object and observes that at points the elevations of the object are 2a 3a respectively shew that AB BG nearly The area of any triangle is to the area of the triangle whose sides are respectively equal to the straight lines joining