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" In any plane 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 Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811
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Handbook of Mathematics for Engineers and Engineering Students

Joseph Claudel - 1906 - 758 pages
...cos q - cos p . 1 . . 1 2 ^ * 2 From the first formula it is seen that the sum of the sines oj two angles is to their difference as the tangent of half the sum oj these angles is to half their difference. 4th. Some other convenient transformations of products,...
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - 1906 - 634 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...
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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)...
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Plane Trigonometry

Fletcher Durell - 1910 - 348 pages
...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...
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Logarithmic and Trigonometric Tables

Fletcher Durell - 1911 - 336 pages
...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...
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Plane and Sperical Trigonometry (with Five-place Tables): A Text-book for ...

Robert Édouard Moritz - 1913 - 562 pages
...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...
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Plane Trigonometry with Tables

Claude Irwin Palmer, Charles Wilbur Leigh - 1914 - 308 pages
...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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Elementary Mathematical Analysis: A Text Book for First Year College Students

Charles Sumner Slichter - 1914 - 520 pages
...- C) c + a tan KC + A) c - a tan i(C - A) 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. GEOMETRICAL PROOP: From any vertex...
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Plane and Spherical Trigonometry

Claude Irwin Palmer, Charles Wilbur Leigh - 1916 - 348 pages
...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...
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Mathematics for Collegiate Students of Agriculture and General Science

Alfred Monroe Kenyon, William Vernon Lovitt - 1917 - 384 pages
...sides arid the included angle are given. 101. 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 a...
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