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Llibres Llibres 151 - 160 de 194 sobre In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions....
" 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 - Pągina 45
per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pągines
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Plane Trigonometry

Webster Wells - 1887 - 103 pągines
...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...
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A Treatise on Mine-surveying

Bennett Hooper Brough - 1888 - 302 pągines
...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...
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Elementary Trigonometry, Plane and Spherical

Edwin Pliny Seaver - 1889 - 284 pągines
...sin AI b =2 R sin B \ ........ [117] 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...
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Elements of Plane and Spherical Trigonometry

Edwin Schofield Crawley - 1890 - 159 pągines
...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...
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A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - 1892 - 368 pągines
...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...
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Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - 1892 - 172 pągines
...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...
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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...
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A Treatise on Plane and Spherical Trigonometry

Ephraim Miller - 1894 - 193 pągines
...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 [31], sin...
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Plane and Spherical Trigonometry

Alfred Hix Welsh - 1894 - 206 pągines
...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...
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New Plane and Spherical Trigonometry

Webster Wells - 1896 - 126 pągines
...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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