Calendar: 1858-1859 Page 427

GENERAL LITERATURE AND SCIENCE 429 If tan θ -- tan tan tan If solid angle be contained by three plane angles any two of them are greater than the third The volumes of similar pyramids are as the cubes of their homologous edges Prove the formula tan Α -f- tan tan Β sin cos θ ן- tan sni -eos If rx and be the radii of the escribed circles touching the two sides of right-angled triangle neither being the hypothe- nuse the area rx r2 Investigate the equation sin -f- sin cos Β -f- sin cos and deduce from it the expressions for sin and cos A- -B The elevation of tower is 30 at point yards nearer it is 45 show that the tower's height -j- si 3J 10 Find sin ha and cos 5a in terms of the sines and cosines of the simple angle and thence deduce the sine and cosine of 36 and 18 11 If be the centre of the inscribed circle show that Ο --- ד co 12 Prove the formula Bx tan -h tan Β cos Β If then cot I- -- sin Β 13 If tan cot find show that sin V5 v5 י 14 Prove the equations cos TJ e-0 sin י 15 Prove that the infinite series Sin £ sin 30 sin &c