 | Elias Loomis - Geometry - 1871 - 302 pages
...^(A+B) . sin. A-sin. B~sin. ^(AB) cos- ^(A+B)~tang. ^(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. COS f*fvt Dividing formula (3) by (4), and considering... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...BCD, being supplements of each other, have the same sine, and BD = a sin. BCD = a sin. C (41) B 102. In any plane triangle, the sum of any two sides is...difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC (Art. 103) be a plane triangle... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...horizontal parallax. PLANE TRIGONOMETRY. 86. Prop.— TJie sum of any two sides of a plane triangle is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. 1 >K\r. — Letting a and b represent any two sides of... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...horizontal parallax. PLANE TRIGONOMETRY. 80. Ргор.— The sum of any two sides of a plane triangle is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. ( DEM. — Letting a and b represent any two sides of a... | |
 | Edward Olney - Trigonometry - 1872 - 216 pages
...horizontal parallax. PLANE TRIGONOMETRY. 86. Prop.— Tlie sum of any two sides of a plane triangle is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. DEM. — Letting a and b represent any two sides of a plane... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...have the following principle : In any plane triangle, the sum of the sides including either angle, is to their difference, as the tangent of half the sum of the two other angles, is to the tangent of half their difference. The half sum of the angles may be found... | |
 | Boston (Mass.). School Committee - Boston (Mass.) - 1873 - 454 pages
...any plane triangle the sides are proportional to the sines of the opposite angles. III. Prove that in any plane triangle the sum of any two sides is...their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. IV. In a triangle the side AB = 532. "... | |
 | New York (State). Legislature. Assembly - New York (State) - 1873 - 818 pages
...(CB); whence we have the principle. When two sides and their included angles are given : The sum of the two sides is to their difference as the tangent of half the sum of the other two angles is to. the tangent of half their difference. This young man also worked out a problem... | |
 | Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 1873 - 352 pages
...the other two sides. Prove it. 5. Prove that in a plain triangle the sum of two sides about an angle is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their diff.rence. 6. One point is accessible and another... | |
 | Aaron Schuyler - Measurement - 1873 - 508 pages
...tan \(A + B) : tan \(A — B). Hence, In any plane triangle, the sum of the sides including an angle is to their difference as the tangent of half the sum of the other tiuo angles is to the tangent of half their difference. We find from the proportion, the equation... | |
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In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... 
