 | Edwin Pliny Seaver - Trigonometry - 1889 - 306 pages
...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... | |
 | Edwin Schofield Crawley - Trigonometry - 1890 - 184 pages
...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... | |
 | William Findlay Shunk - Railroad engineering - 1890 - 360 pages
...any plane triangle, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 4. In any plane triangle, as the cosine of half the difference... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 194 pages
...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... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...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... | |
 | Education - 1892 - 750 pages
...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... | |
 | Ephraim Miller - Plane trigonometry - 1894 - 222 pages
...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... | |
 | Alfred Hix Welsh - Plane trigonometry - 1894 - 228 pages
...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... | |
 | Webster Wells - Trigonometry - 1896 - 308 pages
...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... | |
 | Charles Winthrop Crockett - Plane trigonometry - 1896 - 318 pages
...Two Sides and the Included Angle (b, c, a) . First Method. — The sum of any two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For we have b _ sin ß с sin y By composition... | |
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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... 
