A Synopsis of the Principal Formulae And Results of Pure Mathematics
A Synopsis of the Principal Formulae And Results of Pure Mathematics
Charles Brooke
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2. 3. 4 w". (m~ — 2^)(?». " — 4-) m-. (nr-2-) ^sir (sin 0, ')^ + &c. cos 3a?: cos 5a?: cosy-^'' &c. Cos two; 1.... 6 : cos 0? {1 — 4 (sin a?)"} . : COS . T? { 1 — 12 (sin . Z")- + 16 (sin a?)* } . : cos a- 1 1 - 24 (sin a-)- + 80 (sin a?)^ - 64 (sin . If \ . : &C. =cos, p|l- -^-^(sma?)-+ ^2. 3 A -^''"''•) " ^^j 134 TRIGONOMETIIY. [2] Descending series. 2 cos w . R = (2 cos . ?)" — n (2 cos . R)" " " -\ ' (2 cos x)" " ^ J. . Ji n (7i— 4)(// — 5), ^ 1 03 (2wcosa). « sm wa? = sin X |(2 cos *)" " ^... - !-i-— (2 cos a)» " ^ + 1 Q (2cos. R)"-'^-&c. [ ^ If w is even, the number of terms is iw, and tlie last term, (_l)l«-i. 7i cos X. If n is odd, the number of terms is i(?i + 1, and the last term, (-l)^'"-i>. 2 cos nx = {- 1)'«|(2 sin xy - n (2 sin . R)" " ^ + -—- —
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