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C' (89) (90) (91) (92) (93) 112. 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.
The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 81
by Peter Nicholson - 1823 - 596 pages

## Plane Trigonometry

James Morford Taylor - Plane trigonometry - 1904 - 192 pages
...must deduce other formulas, 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 h (1ff their difference. From the law of sines, we have...

## The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - Engineering - 1902 - 1224 pages
...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)...

## Plane and Spherical Trigonometry

Preston Albert Lambert - Trigonometry - 1905 - 120 pages
...ain(A'-В) = "tan \(A - 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...

## Plane and Spherical Trigonometry

James Morford Taylor - Trigonometry - 1905 - 256 pages
...must deduce other formulas, 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...

## Plane Trigonometry

Plane trigonometry - 1906 - 230 pages
...2 ab cos C These 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...

## Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - Building - 1906 - 620 pages
...2 ab cos C These 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

Fletcher Durell - Plane trigonometry - 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 triangle ABC...

## Logarithmic and Trigonometric Tables

Fletcher Durell - Logarithms - 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 triangle ABC...