Calendar: 1881-1882 Page 638

GENERAL LITERATURE AND SCIENCE 639 angles of depression are found to be 60 and 30 Required the height of the hill 15 Prove the following sin θ tan β cosec0 8ec cot COS0 cos Θ -f- tantf sin β sin20 3tan2 tan20 4cos20 16 ive geometrical proofs for the expansions of the sine cosine and tangent of the sum of two angles in terms of the sines cosines and tangents of the angles 17 Prove and deduce that sin 3a 3sin sin 3λ 8in 30 sin 120 18 Solve the equations sin 3a sin θ cos θ V2 Θ cos 2a co tan Θ tan 19 Prove that in any triangle Bin sin Β -f sin £ £ sin sin 2i -f sin 2C cos cos cos 20 Show how to solve triangle when two sides and the included angle are given 2cos2a ABC cos- cos2 Ex log 80 47712 100 60 tan 10 539-28432 36 21 Explain clearly the ambiguous case in the solution of triangle 4- sin is there any ambigu 22 From the vertex of triangle AD is drawn perpen- dicular to BC and BE from Β perpendicular to AC Show that ABBE may be inscribed in circle and that BE cos