| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| William Mitchell Gillespie - Electronic book - 1868 - 530 pages
...angles are to each other as the opposite sides. THEOREM II. — 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. THEOREM III.— In every plane... | |
| Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 346 pages
...a + I _ tang } (A + B) a — b tang} (A — B) *• ; which shows that, in any triangle, the sum of **two sides is to their difference as the tangent of half the sum of the** angles opposite to those sides is to the tangent of half their difference. We have A + B=180° —... | |
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