Calendar: 1876-1877 Page 584

584 GENERAL LITERATURE AND SCIENCE 14 Prove the formulae co&A sitfA -f sin -f tan2 sec2 coseca see1 cosec2 rf ϊη"Λ cos sin4 Λ cos 15 Determine the values of the trigonometrical ratios for an angle of 30 Prove sin Λ sin 180 sin 180 cos cos 180 cos ISO 16 Trace the changes in the sign and value of cos 3ϊη2Λ as changes from to 360 17 Give geometrical proofs for the expansions of sin cos and tan 18 Solve the equations coti cos β sin 40 eintf and if 7Θ 180 find the value of cos cos 30 cos Ά -f- cos 19 If Β 180 prove sin 2A sin 2B sin 2C 4sin sini sinC cosB cosC cos s'mB sin and thence deduce that the expression sin Λ cot -- sin sinC retains the same value if any two of the quantities ABC are interchanged 20 Prove that in any triangle sin sin Β sin cos Β cos b2 c2 cos 74 Β 2c tan tan -- --