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Llibres Llibres 171 - 180 de 192 sobre In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions....
" In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... "
Elements of Trigonometry: Plane and Spherical - Pągina 45
per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pągines
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The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - 1902 - 1129 pągines
...formulœ enable us to transform a sum or difference into a product. The sum of the sines of two angles is to their difference as the tangent of half the sum of those angles is to the tangent of half their difference. sin A + sin В 2 sin ЩА + B) cos WA - B)...
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Plane and Spherical Trigonometry

Preston Albert Lambert - 1905 - 98 pągines
...B) Since a and b are any two sides of the triangle, in words the sum of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half the difference of these angles. The formula a -H1 _ tan £(A...
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Plane and Spherical Trigonometry

James Morford Taylor - 1905 - 234 pągines
...one of which is the law of tangents below. Law of tangents. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of their opposite angles is to the tangent of half their difference. From the law of sines, we have By...
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - 1906
...formulas are derived in Appendix II. 20. Principle of Tangents. — The sum of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. That is (Fig. 6), a + d _ ta a - b ~ tan...
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Plane Trigonometry

1906 - 188 pągines
...formulas are derived in Appendix ll. 20. Principle of Tangents. — The sum of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. That is (Fig. 6), ab tan i (A - B) The...
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Plane Trigonometry

Fletcher Durell - 1910 - 184 pągines
...sin C' sn . sin В 107 TRIGONOMETRY 75. Law of Tangents in a triangle. In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the angles opposite the given sides is to the tangent of half the difference of these angles. In a triangle ABC (Figs....
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PLANE TRIGONOMETRY

FLETCHER DURELL - 1911
...sin A sin B 107 sin C' TRIGONOMETRY 75. Law of Tangents in a triangle. In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the angles opposite the given sides is to the tangent of half the difference of these angles. In a triangle ABC (Figs....
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Plane and Sperical Trigonometry, with Five-place Tables: A Text-book for ...

Robert Edouard Moritz - 1913 - 453 pągines
...a-6~tan|^-B)' 6-c~tan|(BC)' c+a tang (ü + Л) c- a tan 5 (С - Л) Formulas (7) embody the Law of tangents: In any triangle, the sum of two sides is to their...the tangent of half the sum of the angles opposite is to the tangent of half their difference. The formulas (6), which we shall have occasion to use hereafter,...
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Elementary mathematical analysis: a text book for first year college students

Charles Sumner Slichter - 1914 - 490 pągines
...follows that: b + c _ tan KB + C) _ b - c ~ tan i(B - C) (t)> _ _ _ ca~tani(CA) (l)) Expressed in words: In any triangle, the sum of two sides is to their...the tangent of half the sum of the angles opposite is to the tangent of half of their difference. GEOMETR1CAL PBOOF: From any vertex of the triangle as...
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PLANE TRIGONOMETRY WITH TABLES

CLAUDE IRWIN PALMER - 1914
...solution by logarithms the following theorem is needed: TANGENT THEOREM. In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. „ „ a sin a: f . ,, Proof. T = - —...
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