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 Llibres Llibres 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... Elements of Trigonometry, Plane and Spherical - Pàgina 43
per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pàgines
Visualització completa - Sobre aquest llibre ## Plane Trigonometry

Webster Wells - 1887 - 103 pàgines
...expressed more compactly as follows: ab с sin , I sin Б sin С 114. 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. Formula (45) of Art. 113 may be put in...
Visualització completa - Sobre aquest llibre ## A Treatise on Mine-surveying

Bennett Hooper Brough - 1888 - 302 pàgines
...known, and it is required to find the two other angles, and the third side. In this case, the sum of the two sides is to their difference, as the tangent of half the sum of the two unknown angles is to the tangent of half their difference. Half their difference thus found, added...
Visualització completa - Sobre aquest llibre ## Elementary Trigonometry, Plane and Spherical

Edwin Pliny Seaver - 1889 - 284 pàgines
...sin AI b =2 R sin B \ ........  с =2 Л sin С i 179. The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite anyles is to the tangent of half their difference. ANALYTIC PROOF. The first two equations...
Visualització completa - Sobre aquest llibre ## Elements of Plane and Spherical Trigonometry

Edwin Schofield Crawley - 1890 - 159 pàgines
...can show and sin B sin C ca sin C sin A. abc sin A sin 5 sin C . ч (82) or PLANE TIUGONOMETKY. 62. In any triangle the sum of two sides is to their difference ae the tangent of half the sum of the opposite angles is to the tangent of half their difference. From...
Visualització completa - Sobre aquest llibre ## A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - 1892 - 368 pàgines
...difference, provided the right order is maintained. 97. Law of Tangents. — 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. By Art. 95, a : b = sin A : sin B. By composition...
Visualització completa - Sobre aquest llibre ## Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - 1892 - 172 pàgines
...difference, provided the right order is maintained. 57. Law of Tangents. — 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. By Art. 55, a : b = sin A : sin B. By composition...
Visualització completa - Sobre aquest llibre ## The Ohio Educational Monthly and the National Teacher: A Journal ..., Volum 41

1892
...solving triangles ? 2. Prove: — 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. 3. Find the sine of half an angle in terms...
Visualització completa - Sobre aquest llibre ## A Treatise on Plane and Spherical Trigonometry

Ephraim Miller - 1894 - 193 pàgines
...multiplied (1) by a, (2) by b, and (3) by — c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, the sum of two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their differenve. From the fundamental formulae , sin...
Visualització completa - Sobre aquest llibre ## Plane and Spherical Trigonometry

Alfred Hix Welsh - 1894 - 206 pàgines
...CB + AB : CB - AB : : tan ^ (A + Cf) : tan £ (A - C). Hence, 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. Scholium. — The half difference added...
Visualització completa - Sobre aquest llibre ## New Plane and Spherical Trigonometry

Webster Wells - 1896 - 126 pàgines
...с = sin В : sin C, and с : a = sin (7 : sin A. (48) (49) 108. In- a iti/ 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. By (47), a:b = sin A : sin B. Whence by...
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