82 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



n cos (n + i)x-sm nx 



2 sn x 



cos (n + i)#-sin 



2 sn x 



n i 



X^ , , , sin nx 

 5. 7, k sin kx = 



(2n-I\ 



wcos (~^r 



k= T 4 siir- 2 sin - 



. (2n - i\ 

 n sin ( jx 



ni 

 _ . . . " ." I - COS 



6. 



~T. 2 sm - 4 sm 2 - 



2 2 



7. . Sin 2 IjiC = : 



1 J sm x 



ft-i 



n 



8. 2 s i n (* + 



k = 



n 



9. /^ cos 



k=o 



n+i 



10. 



COS 



2 COS 



vfc ci'n z,^ _ r sn ^ ~ rn cos ~ T ~ ^ cos o;r M sin nx 



/ Sill KOC "~ ~ 



i 2r cos x + r 2 



fc , (i - r cos x) (i - r n cos nx) + r n+1 sin x sin w 



* ^ ^** ~~ " o 



i - 2r cos ac + r 2 



14. / . ( . sec , ) = esc 2 x ( esc ) 



j\2 k 2*7 \2 n 2 n J 



X \ 2 / iC \ 2 



in2 if) = I 2 n sin ?J ~ sin2 * 



