 | James Morford Taylor - Trigonometry - 1905 - 256 pages
...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... | |
 | International Correspondence Schools - Building - 1906 - 620 pages
...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... | |
 | Plane trigonometry - 1906 - 230 pages
...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... | |
 | Fletcher Durell - Plane trigonometry - 1910 - 348 pages
...collecting results, ab с 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...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.... | |
 | Fletcher Durell - Logarithms - 1911 - 336 pages
...collecting results, a 1} c 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...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.... | |
 | Robert Édouard Moritz - Trigonometry - 1913 - 560 pages
...(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 difference as 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,... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Plane trigonometry - 1914 - 308 pages
...Second method. — For a 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 = - —... | |
 | Charles Sumner Slichter - Functions - 1914 - 516 pages
..._ 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 difference, as 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... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...Second method. — For a 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 sina Proof. r = -. — -, from sine theorem.... | |
 | William Charles Brenke - Trigonometry - 1917 - 200 pages
...sides minus twice their product by the cosine of their included angle. Law of Tangents. — The sum of 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. Half Angles. — The sine of half an angle... | |
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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... 
