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In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ... - Page 12
by Francis Nichols - 1811 - 128 pages

## Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...(45° -A) =2 tan 2 A. 5. In any triangle, calling one side the base, prove that the sum of the other two sides is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. 6. Observers on two ships a mile apart...

## Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference is...

## Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...£ (^l — " B) (R7\ smA—maB ~ <^rt1[ (A + B) ' *•"' that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to tlie tangent of half their difference, or as the cotangent of half their difference is...

## Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1862 - 414 pages
...AC . : sin C : sin B. THEOREM IL In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of tt1e two oif1er angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will...

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...cot | (A — B) . . sin "A ^^sin "B ~ cot ±1 (A^~B) ' that is, The sum of the sines of two angles is to their difference as the tangent- of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference is...

## Calendar of the McGill University, Montreal

McGill University - 1865 - 332 pages
...latter formula, determine tan. 15°, first finding tan. 30°. 5. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the base angles is to the tangent of half the difference. 6. Prove that if A" be the number of seconds...

## Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...(A+B) : cos. A+sin. B :: cos. A— sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)...

James Pryde - Navigation - 1867 - 506 pages
...add the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being added,...