# Calendar: 1875-1876 Page 584

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580 GENERAL LITERATURE AND SCIENCE 13 The angles of triangle are in harmonic progression ami the number of grades in the least the circular measure of the greatest 40 π Find the angles 14 Trace the changes in sign and magnitude of sine cos 2Θ as θ changes from to 7r Shew that sec θ bf is only possible when 15 Prove that aa 2tan0 tan θ tan Find tantf in terms of tan 20 and explain the ambiguity of sign Apply tbe formula to find tan 15 16 Solve the equations β cos0 sec θ 2sin 5sin0 sin0 cos V2 and shew that sin sin ηθ sin 2m -- י-י-ί tan η coso cos ηθ cos 20 -1ן 17 If Β ISO" then sin 2A -f sin 25 2C 4sin sin Β sin Β π-Α π-Β π-C III cos -4 cos -4- cos cos---cos--COS- 18 The elevation of tower standing on horizontal plane is observed feet nearer to the tower the elevation is found to he 45 feet nearer still the elevation is the complement of what it was at the first station Find the height of the tower 19 Shew that in any triangle ABC cos Β cos

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