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" B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B... "
Elements of Geometry and Trigonometry - Page 225
by Adrien Marie Legendre - 1838 - 269 pages
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Examinations Papers

1891 - 644 pages
...bisectors of the sides of a triangle meet in. a point of trisection of each. 7. Establish the formulse cos ( A — B) •=. cos A cos B + sin A sin B and cos A — cos B z= 2 sin — ~^ — sin c 8. Show that A sin 9 + B cos 6 can always be put in the form...
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Trigonometry for Beginners

John Bascombe Lock - Logarithms - 1896 - 242 pages
...deduce the formula tan (180° + A) = tan A. 81. Compute by means of tables the value of 82. Prove that cos (A + B) = cos A cos B — sin A sin B, and deduce the expression for sin (A + B). 83. Establish the identities : (1) 1 + савА-вшА= V2(l...
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Plane Trigonometry: An Elementary Course Excluding the Use of Imaginary ...

Sidney Luxton Loney - Plane trigonometry - 1896 - 344 pages
...sm(4 + ß)-sin(J.-Д) = 2cosJ.sin.ß (2). From the same articles we have, for all values of A and Д cos (A + B) = cos A cos B — sin A sin B, and cos (A — B) = cos A cos B + sin A sin A Hence, by addition and subtraction, we have cos (A + B) +...
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Calendar, for the Year ...

1899 - 166 pages
...72, 48, . . . to « terms and to infinity. 8. Prove geometrically — (i) 1 +cot2O = conec3O ; (ii) cos (A + B) = cos A cos B - sin A sin B ; and from (ii) deduce cos 15° and cos 75°. i). Express sin A in terms of tan A. The two sides of a right-angled...
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The Ohio Educational Monthly, Volume 55

Education - 1906 - 860 pages
...(1) sin A= V 1 — cos* A. 1 _ (2) cos A = j/1 + tan1 A. If sec A = i/ 2, find tan A. 5. Prove that cos (A + B) =cos A cos B • — sin A sin B and cos (A + B + C) -- = cot A cot B cot C sin A sin B sin C — cot A — cot B — cot C. 6. Show that...
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Elementary Trigonometry

William Ernst Paterson - Logarithms - 1911 - 262 pages
...having the angle at P equal to A° ; PQ is inclined to OX at an angle B°. Prove by projection that cos (A + B) = cos A cos B — sin A sin B, and sin (A + B) = sin A cos B + cos A sin B. 70. If the projections of a line on two lines at right angles...
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Journal of Education

Education - 1911 - 1334 pages
...quality of composition. TRIGONOMETRY.— XII. 3 to 5 pm, Friday, 27th June, 1913. 1. Prove the identity: cos. (A — B) = cos. A cos. B + sin. A sin B, and by using it, find the numerical value of cos. 15°. 2. Find value of tan. 2 A in terms of tan. A; and...
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A Treatise on Plane Trigonometry

Ernest William Hobson - Exponential functions - 1911 - 432 pages
...the generality of the proof. If we change В into — B, in each of the formulae (1) and (2), we have cos (A — B) = cos A cos (— B) — sin A sin (— B) and sin (A — B) = sin A cos (— B) — cos A sin (— B), hence cos (A - B) = cos A cos В + sin A sin...
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Special Reports on Educational Subjects, Volumes 26-27

Great Britain. Board of Education - Education - 1912 - 1044 pages
...all the values of 9, between 0° and 360°, which satisfy the equation sin 6 = cos 49 6. Prove that cos (A + B) = cos A cos B — sin A sin B and that cos A + cos B = 2 cos — T — cos — ^ — Prove that, if A + B + C — 90°, then 4 cos ?-£-?...
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A Manual of Field Astronomy

Andrew Hall Holt - Geodetic astronomy - 1916 - 152 pages
...sin s • sin p sin s • sin p + cos ^ • cos p — cos z sin s • sin p From plane trigonometry: cos ( A — B ) = cos A • cos B + sin A • sin B and: 2 sin2 A/2 = 1 — cos A Substituting: . Z cos (s — p) — cos z 2 sin2 — = - ; 2 sin s • sm...
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