 | Charles Hutton - Mathematics - 1812 - 624 pages
...trigonometry. 27. Once more, dividing the expression for sin (A ± B) by that for cos (A ± B), there results sin (A ± B) _ sin A . cos B ± sin B . cos A _ cos (A + B) cos A . cos B q: sin A . sin B " then dividing both numerator and denominator of the... | |
 | Sylvestre Francois Lacroix - Geometry, Analytic - 1827 - 350 pages
...~ cos a + cos b'' 6°. En divisant l'expression de sin (a ± è) par celle de cos (a ±è), on aura sin (a ± b) _ sin a cos b ± sin b cos a cos (a ± è) cos a cos è qr sin a sin 6 DiVisant ensuite le numérateur et le dénominateur de la... | |
 | John Radford Young - Astronomy - 1833 - 286 pages
...— sin.B) cos.(A + B)cos.(AB)=cos.2B-sin.2A=(cos.B+sin.A)(cos.B-sin.A) 4. By division, sin. (A + B) sin. A cos. B + sin. B cos. A sin. ( A — B) sin. A cos. B — sin. B cos. A cos. ( A + B) cos. A cos. B — sin. A sin. B cos. (A — B) cos. A cos. B... | |
 | Charles Bonnycastle - Geometry - 1834 - 670 pages
...— tan. c , . (8). . tan. b = - = tan. (a — c) 1 + tan. a tan. c The equations sin. (a + b) •= sin. a cos. b + sin. b cos. a sin. (a — b) = sin. a cos. b — sin. b cos. a which are the same with 3 and 7, give, by addition and subtraction, (9) .... | |
 | Military art and science - 1836 - 426 pages
...exprimés par les équations suivantes qu'on a reconnues avoir lieu pour des arcs de grandeur quelconque : •sin. a cos. b + sin. b cos. a sin. (a + b) = £ sin. a cos. b — sin. b cos. a sin. (a — b} cos. (a + b} = cos. (a — b} = R cos. a cos. b — sin. a... | |
 | Charles Davies - Calculus - 1836 - 296 pages
...differential of the sine of an arc. For this purpose we will assume the formulas (Trig. Art. XIX), sin a cos b + sin b cos a sin (a + b) = sin (a — b) — R sin a cos b — sin b cos a R If we subtract the second equation from the first, 2 sin... | |
 | Bourdon (M., Louis Pierre Marie) - Geometry, Analytic - 1837 - 700 pages
...dans les applications trigonométriques. Reprenons d'abord les formules (A) , savoir : sin (a + b} = sin a cos b + sin b cos a, sin (a — b) = sin a cos b — sin b cos л. Ces formules combinées successivement par addition et par soustraction, donnent... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...cosines of Л -\- В and A — B, expressions for the tangents of A + В and A — B. Thus, Т ( A A- TVi sin.' (A + B) _ sin. A cos. B -\- sin. B cos. A * ' ' cos. (A + B) cos. A cos. В — sin. A sin. В Divide both numerator of this fraction by cos.... | |
 | Pierre Jules Meunier-Joannet - 1858 - 450 pages
...cos a. T8 ( w - a ) - - Tg a. sin ( — a ) zz — sin a. cos ( — a ) = cos a . ' sin ( o + b ) = sin a cos b + sin b. cos a. sin (a — b ) = sin a cos fc — sin 6. cos a. cos ( a + 6 ) = cos a cos 6 — sin a. sin b. cos (a — 6 ) =. cos a cos... | |
 | Elias Loomis - Conic sections - 1880 - 452 pages
...of their difference as the sum of the tangents of those arcs is to the difference of the tangents. sin. (a — b) _ sin. a cos. b — sin. b cos. a _ tang. a — tang. b cos. a cos. b R cos. a cos. b R2 -* that is, The sine of the difference of two... | |
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By division, sin. (A + B) sin. A cos. B + sin. B cos. A sin. ( A — B) sin. A cos. B — sin. B cos. A cos. 
