BOOK OF MATHEMATICAL PP.OBLEMS. 

 393. Prove that 



^.-jg-^y -^U.-.tooo 



394. Prove that 



tan _J 1 



80 TT' - 40" T (37r) 8 - 40 s (Sir) 8 - 40 8 T 



395. Prove that if be an angle between - and - T . 



4 4 



. 2 sin 4 . 2.4 sin 6 2.4.6 sin 8 



396. Prove that 



_-l 



n T 0~0 i 



397. The expansion of tan tan tan x is 



x + 2w ^ + in (5n - 1) -^ + ^ (350^ - 168/1 + 22) 4 + 

 jo o o 1 7 



the tangent being taken n times. 



VII. Series. 



In the summation of many Trigonometric series in which the 

 r^ term is of the form a r cos rO, or a r sin rO, a r being a function 

 of r, it is convenient to sum the series in the manner following. 

 "To find the sum of 1 + 2 cos 6 + 3 cos 20 + ... + n cos (n- 1) 0." 



Let C = 1 + 2 cos + 3 cos 20 + . . . + n cos (w - 1) \ 

 and = 2 sin + 3 sin 20 + ... + n sin (w- 1) / ' 

 and let cos + J(- 1) sin = z. 





