| 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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