214 BOOK OF MATHEMATICAL PROBLEMS. 



where x l = r sin 0, cos 2 , x a = r cos 6 l cos a , 



x t = r sin t sin O a cos 4 , ce 4 = r sin 0, sin 6 a sin 

 o; 6 = r cos X sin O a cos 5 , o: fl = r cos t sin 3 sin 



1029. Prove that 



is equal to 



the limits being given by the equation, 



1030. Prove that the limit of the sum of the series 



la? 1 x 6 

 *- + -- *' 



when x is indefinitely increased is ^ . 



1031. Prove that, if n be a positive integer r 



and that 



1032. Prove that 



(1) I sin 4aj log cot xdx = -~ , 







STT 



fljcosa? . or 



1 + sin* x 2 ' 







