 | Robert Woodhouse - Geometrical optics - 1819 - 470 pages
...by the cosine, if the arc be A ± B, tan (A 4- Jf\ — s'n' (^ i~ -^ — s'n' ^ • cos> В ± cos. A . sin. В ~~ cos. (A + }B cos. A • cos. В + sin. A . sin. ß Now, since the object is to obtain an expression involving tan. A, tan. B, we must divide both numerator... | |
 | John Radford Young - Calculus, Integral - 1833 - 320 pages
...Required the integral of sin. M r sin. nx dx. Since by Trigonometry cos. (A — B) = cos. A cos. В + sin. A sin. В cos. (A + B) = cos. A cos. В — sin. A sin. В .-. - cos. (A — B) — - cos. (A + B) = sin. A sin. B, or, substituting mx for A and nx for B, we have sin. mx sin. nx = - cos. (m —... | |
 | John Radford Young - Astronomy - 1833 - 308 pages
...sin. ( A + B) = sin. A cos. В + sin. В cos. A ' »in. (A — B) = sin. A cos. В — sin. B cos. cos. (A + B) = cos. A cos. В — sin. A sin. В cos. (A — B) = cos. A cos. В From these equations we get 1. By addition, .A, •A> iin. A sin. В ") > • • • • (2)in. A... | |
 | John Martin Frederick Wright - Mathematics - 1836 - 698 pages
...dc + JJ- xdx i* o ' " I — ~' ~ / — ?= J «yi + я2 JV 1 = I. (-r both being common forms. 519. cos. (A— B) = cos. A. cos. В + sin. A. sin. В...cos. (A + B) = cos. A. cos. В — sin. A. sin. B> Л cos. (A- B) - cos. (A + B) =: 2 sin. A. sin. В Let A= mo, B = n Q Then dô sin. mo- sin. n Q =... | |
 | James Hann - Plane trigonometry - 1854 - 140 pages
...В (4). By subtraction, cos (A - 5) - cos (A +B) = 2smA sin Б ,.(5). By multiplication, cos (A + B} cos (A - B) = cos' A cos* В - sin" A sin' В = cos* A (1 - sin2 B) - sin' В (I- cos' A) = cos2 A — sin2 В = (cosA + sin B) (cos A —sin В) (6). Now... | |
 | Alexander Hadden Hutchinson - 1861 - 128 pages
...the arithmetical progression 1, 3, 5, 7, ... 3. Prove the formules sin (A + B) — sin A cos В + cos A sin В cos (A + B) = cos A cos В — sin A sin B. Find the sine and cosine of 15°. 4. Prove that sin 4A = 4 sin A cos3A — 4 cos A sin3A. 5. A line... | |
 | Isaac Todhunter - Plane trigonometry - 1874 - 360 pages
...sum or half the difference of two such Ratios. 8r Т (A r>\ _^°- (^- + Б) _sm A cos, В + сов, A sin В ^ cos (A + B) ~ cos A cos В — sin A sin В ' divide both numerator and denominator of the last expression by sin A sin В . _ , cos .4 cos... | |
 | Thomas Kimber - 1874 - 352 pages
...В — cos. A . sin. B, adding we get sin. (A + B) + sin. (A — B) = 2 sin. A . cos. В (P) Again, cos. ( A + B) = cos. A . cos. В — sin. A . sin. В cos. (4 — B) = cos. J . cos. В + sin. 4 . sin. B. .-. cos. (-4 + B) + cos. (A — B) = 2 cos. A . cos.... | |
 | Edward Atkins - 1875 - 410 pages
...l-2sin2|- (4). 5. To find tan (A ± B), cot (A ± B). , / A + B^ — s*n (A ± B) _ sin A cos В ± cos A sin В cos (A ± B) cos A cos В + sin A sin В sin A + sin В cos A ~ cos В 1 _ sin A sin В cos A ' cos В tan A ± tan В ,,. Г? tan A tan... | |
 | John Bascombe Lock - Logarithms - 1896 - 244 pages
...В (i.) By using the results of Arts. 76, 77, we have ,,. — sin (Л 4. B) — sin A , cos В + cos A , sin В cos (A + B) ~ cos A , cos В - sin A , sin В Divide the numerator and the denominator of this fraction each by cos A , cos B, and we get sin... | |
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В sin (A — B) = sin A cos В — cos A sin В cos (A + B) = cos A cos В - sin... 
