V . . / N 2 ni in — I

2*"( — i)"sm^''.r ^= 2cos2/i.r — 2.2/1 cos (2/1 — ijx H- 2. — ^ cos (2/1 — 4)-^- • •

, , iniin — i)...[n-\-\]

2'"+'( — i)"sin2"+'.r r= 2sin(2/i + i) x' — 2(2/? + i)sin(2/i — \)x -\-. . .-

, , (2/1 H-l) 2/1. . .(/? H- 2I . H- 1)''.2 ■ ^SUlcT.

Ces formules étant souvent utiles, nous donnons ici les valeurs numériques des coefficients pour les cas les plus simples; on a :

2 cos' .r = cos 2 jc H- I ,

4 cos' .r = cos 3 .r H- 3 cos ^,

8cos^,r = cos4.^ + 4 fOS2.r i6cos*^ = cos5.r 4- 5cos3.îlr- 32 cos^^jc = cos6^ -i-6cos4-^ - 64 cos':t:= COS7X-I- 7 cos5.r 128 cos^o: = cos8^ 4- 8cos6^ H- 28 cos4^ + 56 cos2^ -h 35,

— 2sin^.r = cos2.r — i,

— 4 sin' .r = sin3ji; — 3 sin x, + 8 sin* 37 = cos4^ — 4cos2.r+ 3,

i6sin*jj;=sin5.r — 5 sin 3^ -f- 10 sin^, — 32sin''ji7 = cos6a: — 6 cos 4^ -H i5 cos 2^ — 16, — 64sin'.r=sin7,r — 7sin5.^-f-2i sin3^ — 35sin.r, 1 28 sin* ^ = cos 8 .r — 8cos6^ + 28cos4.^ — 56cos2^.

10 cos,r,

i5 C0S2jr H- lo,

21 cos3^-l- 35

cosjr,